Fiveable
Fiveable

or

Log in

Find what you need to study


Light

Find what you need to study

6.5 Images from Lenses and Mirrors

10 min readjanuary 8, 2023

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

Images From Lenses and Mirrors

Let’s talk about mirrors, optical devices that form images by reflecting light. We’ve all looked into a mirror and seen images of our faces and nearby objects; in this section, we’re going to analyze those images mathematically.


Plane Mirrors

are flat mirrors, and they’re the simplest type of mirror. Now, how is an image of an object in a mirror even formed? Well, light that’s reflected off of the object hits the mirror and reflects back into our eyes. The direction of the reflected rays determine where we perceive the image of the object to be.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-YXue9Oa4Ua0b.png?alt=media&token=e4f8ad79-7bd2-47cc-a116-c6049ff1e20e

Taken from Wikimedia Commons

We’re going to dive into the image characteristics of by answering the following questions:

1. Where’s the image, and how does the height of it compare with the object’s?

2. Is the image real or virtual?

3. Is the image upright or inverted?

(1) Think back to when you look at yourself in a flat mirror; it seems as if the image of yourself is behind the mirror. When you take a step sideways, the image of you also steps sideways. The image seems as far behind the mirror as the object is in front of the mirror(the can be used to show this). In a flat mirror, the image isn’t enlarged or shrunken compared to the size of the object.

(2) First off, what does it mean for an image to be real or virtual? An image is real if the light rays actually focus at the image; the light converges and passes through the actual image location. For flat mirrors, the image is virtual: light rays don’t actually pass through the image location on the other side of the mirror.

(3) Once again, re-imagine looking at yourself in a flat mirror. Your image isn’t upside down; it’s upright. Question 3 answered.

Check out this interactive to really solidify your understanding of .


Concave Mirrors & Convex Mirrors

Concave and are , mirrors that are specifically curved so that their surfaces form part of a sphere.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-aR7aEfVlvhli.png?alt=media&token=5dbbe5c4-91ae-45d4-a016-0a7582a0b904

Taken from Wikimedia Commons

  • The line that passes through the center of the surface and the center of curvature of a spherical mirror.
  • Center of Curvature (C)—The center of the imaginary sphere from which the section of the mirror was cut from.
  • Radius of Curvature (R)—The radius of the imaginary sphere.
  • Focal Point (Focus)—The point halfway between the center of curvature and mirror.
  • Focal Length (f)—The distance from the mirror to the focal point.
  • Vertex (V)—The intersection of the with the mirror; it’s also the geometric center of the mirror.

The focal length is one-half of the the radius of curvature:

f=R/2

The image above was a concave mirror; the reflective side is caved in towards the center of curvature. The following image is a convex mirror; the reflective side curves away from the center of curvature.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-kcplQQpG44Zj.png?alt=media&token=9508e4e6-4381-4124-8989-04f6abb8f210

Taken from Wikimedia Commons


Ray Tracing for Mirrors

is an essential tool that helps us determine the location of the image. We draw representative light rays in a diagram along with the object and the mirror: the point at which the reflected rays intersect is the location of the image. Let’s go over some of the rules:

Here are the steps for for mirrors:

  1. Draw a diagram showing the position of the mirror and the location of the object.
  2. Draw two rays emanating from the top and bottom of the object and reflecting off the mirror.
  3. Predict the path of the rays after they reflect off the mirror using the laws of reflection.
  4. Determine the location of the image by finding the intersection of the two rays.
  5. Determine the size and orientation of the image by comparing the object and the image.

:

  • An incident ray parallel to the is reflected through the focus.
  • An incident ray that travels through the focus is reflected parallel to the .
  • An incident ray that goes through the vertex is reflected at an equal angle to the .
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-9TNcbTX3yea5.png?alt=media&token=9bb45e57-7d52-43e1-b941-40b2b20d2f2f

Taken from Wikimedia Commons

:

  • An incident ray parallel to the is reflected in a way such that its extension passes through the focus.
  • An incident ray that travels through the focus is reflected parallel to the .
  • An incident ray that goes through the vertex is reflected at an equal angle to the .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-zEthWEYZ2i4a.png?alt=media&token=183886b7-714e-4ebe-b0da-6bfe63698b80

Taken from Wikimedia Commons

With , if the image is on the same side of the mirror as the object, then the image is real; if it’s formed on the opposite side, it’s virtual. Other aspects of the image (its size, location, orientation) can be also determined by . It might be a little tricky at first, but with practice, it'll get easier.


To answer our questions about images in an easier and faster way, we can use two equations. The first is the :

1/f=1/d_o+1/d_i

  • d_o​: the object’s distance from the mirror
  • d_i​: the image’s distance from the mirror

To differentiate mathematically between concave and convex, we set the focal length to the following:

  • For , f is positive value
  • For , f is negative value

The second equation is the :

M=-d_i/d_o=h_i/h_o

h_i​: height of image

h_o​: height of object

  • If d_i​ positive, then M is positive: the image is upright.
  • If d_i​ negative, then M is negative: the image is inverted.
  • If M<1, the image is reduced.
  • If M>1, the image is enlarged.
  • If M=1, the image is the same size as the object.

Keep in mind that all real images are inverted and all virtual images are upright.


Converging Lenses & Diverging Lenses

Lenses are optical devices that form images by refracting light. There are 2 types of lenses: converging and diverging.

Converging (convex) lens—converges parallel light rays to a focal point on the far side.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-jYe7GdgVeUET.png?alt=media&token=23b2e366-2dd7-40e6-bc59-e72e8fef1092

Taken from Wikimedia Commons

Diverging (concave) lens—causes light rays to diverge away from a focal point on the same side as the incident rays.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Rp7XhR39ZJvz.png?alt=media&token=b1ef94fd-1374-4645-9a2c-2a2398423c4b

Taken from Wikimedia Commons


Ray Tracing for Lenses

Just as we did with mirrors, we can use with lenses to get information about an image. Let’s go over the rules for for lenses:

Here are the steps for for lenses:

  1. Draw a diagram showing the position of the lens and the location of the object.
  2. Draw three rays emanating from the top, middle, and bottom of the object.
  3. Draw the first ray parallel to the optical axis and predict its path after it passes through the lens using the lens equation.
  4. Draw the second ray through the center of the lens and predict its path after it passes through the lens using the lens equation.
  5. Draw the third ray through the focal point of the lens and predict its path after it passes through the lens using the lens equation.
  6. Determine the location of the image by finding the intersection of the three rays.
  7. Determine the size and orientation of the image by comparing the object and the image.

Convex Lenses:

  • An incident ray traveling parallel to the is refracted through the focus.
  • An incident ray passing through the focus refracts through the lens and travels parallel to the .
  • Incident rays that travel through the center point of the lens pass undeflected.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-yKjqXDDDn1hX.png?alt=media&token=f892df27-3c3a-41dd-894f-dc053a180f99

Taken from Wikimedia Commons

Concave Lenses:

  • An incident ray traveling parallel to the axis refracts through the lens and travels in line with the focal point.
  • An incident ray passing through the focal point refracts through the lens and travels parallel to the .
  • Incident rays that travel through the center point of the lens pass undeflected.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-0iAKm2eHnJuJ.png?alt=media&token=84b8e0aa-43ce-4087-bc5e-36256c9ab2dc

Taken from Wikimedia Commons


The Equations of Lenses

Lens and mirrors use the same equations! Just keep in mind that:

  • Converging optical devices(+f): and convex lenses
  • Diverging optical devices(-f): and concave lenses

Some simulations to check out for lenses and mirrors:

Optics Bench Interactive

Concave Mirror Image Formation

Convex Mirror Image Formation

Converging Lens Image Formation

Diverging Lens Image Formation


Practice Problems

1. A plane mirror produces an image that is:

A) real, inverted, and larger than the object.

B) real, upright, and the same size of the object.

C) real, upright, and smaller than the object.

D) virtual, inverted, and smaller than the object.

E) virtual, upright, and the same size as the object.

2. An object is located 0.20 meters from a converging lens which has a focal length of 0.15 meters. Relative to the object, the image formed by the lens will be:

A) real, erect, smaller

B) real, inverted, smaller

C) real, inverted, larger

D) virtual, erect, larger

E) virtual, inverted, smaller

3. A narrow beam of monochromatic light enters a lens parallel to the optic axis, as shown in the accompanying diagram. Which arrow best represents the direction of the light after leaving the lens?

A) A

B) B

C) C

D) D

E) E

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-rwVUO1eYpnU3.png?alt=media&token=249480cc-0ba6-4f1d-a6b9-8c63c6f34e75

4. A beam of light traveling in glass (n_gng​ = 1.5) strikes a boundary with air (n_ana​ = 1.0) at point P. The angle of incidence is 60° as shown in the diagram. Which ray would best indicate the beam’s path after point P?

A) A

B) B

C) C

D) D

E) E

5. An object is placed 10 cm in front of the center of a concave curved mirror with a radius of curvature of 10 cm. About how far from the mirror will the real image of the object be formed?

A) 0 cm

B) 5 cm

C) 10 cm

D) 20 cm

E) No image is formed

6. A diverging lens produces an image of a real object. This image is

A) virtual, larger than the object, and upright

B) virtual, smaller than the object, and upright

C) virtual, smaller than the object, and inverted

D) real, smaller than the object, and inverted

7. An illuminated object is placed 0.30 meter from a lens whose focal length is –0.15 meter. The image is

A) inverted, real, and 0.30 meter from the lens on the opposite side from the object

B) upright, virtual, and 0.30 meter from the lens on the opposite side from the object

C) upright, real, and 0.10 meter from the lens on the same side as the object

D) upright, virtual, and 0.10 meter from the lens on the same side as the object

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Vl1wN18obp6h.png?alt=media&token=caf589d4-61e4-40b8-a661-dbd34648504c

Use the Figure above for questions 8 and 9. An object O is located at point P to the left of a converging lens, as shown in the figure. F_1F1​ and F_2F2​ are the focal points of the lens.

8. If the focal length of the lens is 0.40 m and point P is 0.30 m to the left of the lens, where is the image of the object located?

A) 1.2 m to the left of the lens B) 0.17 m to the left of the lens C) At the lens D) 0.17 m to the right of the lens E) 1.2 m to the right of the lens

9. Which of the following characterizes the image when the object is in the position shown?

A) Real, inverted, and smaller than the object B) Real, upright, and larger than the object C) Real, inverted, and larger than the object D) Virtual, upright, and larger than the object E) Virtual, upright, and smaller than the object

10. A physics student places an object 6.0 cm from a converging lens of focal length 9.0 cm. What is the magnitude of the magnification of the image produced?

A) 0.6

B) 1.5

C) 2.0

D) 3.0

E) 3.6


Answers:

  1. E: always makes virtual, same size, upright images

  2. C: Using the math, 1/f = 1/do + 1/di, and M = – di / do … di +0.6 M = – 3 …

  3. E: A horizontal beam approaching a converging lens bends and converges through the focal point

  4. E: Generally when we go from more–less we should always check the critical angle first rather than assuming the ray will refract and bend away. Choice D might be correct, but not until we first check the critical angle for total internal reflection. Use ni sin θc = nr sin (90), ni=1.5, nr=1θc = 41.8°. Since our incoming angle (60) is larger than the critical angle, total internal reflection will occur and you will get choice E.

  5. C: The focal point is = R/2. Then use the math 1/f = 1/do + 1/di … and di = 10

  6. E: Fact about diverging lens.

  7. D: Using the math, 1/f = 1/do + 1/di, and M = – di / do … di = – 0.10 m, M = +0.33

  8. A: Using the math, 1/f = 1/do + 1/di, di = –1.2. Its virtual so its on the same side as the object, which puts the image on the left side of the lens

  9. D: This is a magnifying glass, which can be memorized or the math can be done to prove the answer

  10. D: Using the math, 1/f = 1/do + 1/di, di = –18 … then M = – di / do … M = 3


Key Terms to Review (19)

Center of Curvature (C)

: The center of curvature is the center point of a sphere from which a curved mirror or lens is derived.

Concave lens

: A concave lens is a lens that is thinner in the middle and thicker at the edges, causing light rays to diverge when passing through it.

Concave Mirrors

: Concave mirrors are mirrors that curve inward, causing light rays to converge at a focal point. They are often used in telescopes and makeup mirrors.

Converging Lenses

: Converging lenses are lenses that are thicker in the middle and cause parallel light rays to converge or come together at a focal point after passing through the lens.

Convex lens

: A convex lens is thicker in the middle than at its edges and converges parallel rays of light that pass through it, bringing them together at a focal point.

Convex Mirrors

: Convex mirrors are mirrors that curve outward, causing light rays to diverge. They have a wider field of view but produce smaller images compared to concave mirrors. They are commonly used in car side-view mirrors.

Diverging Lenses

: Diverging lenses are lenses that are thinner in the middle and cause parallel light rays to spread out or diverge after passing through the lens.

Focal Length (f)

: The focal length is the distance between the center of a lens or mirror and its focal point. It determines how much a lens bends light and affects image formation.

Focal Point (Focus)

: The focal point, also known as the focus, is the point on the principal axis where parallel rays of light converge or appear to diverge from after passing through a lens or reflecting off a mirror.

Law of reflection

: The law of reflection states that the angle of incidence (the incoming angle) is equal to the angle of reflection (the outgoing angle) when light reflects off a surface.

Magnification Equation

: The magnification equation is an equation that relates the height of an image to the height of the object. It helps determine whether an image is magnified or reduced in size.

Mirror equation

: The mirror equation is a mathematical relationship that relates the object distance (distance of an object from a mirror), the image distance (distance of the image from the mirror), and the focal length of a mirror.

Plane Mirrors

: Plane mirrors are flat, smooth surfaces that reflect light in a predictable way. When light rays hit a plane mirror, they bounce off at the same angle they hit the mirror.

Principal Axis

: The principal axis is an imaginary line that passes through the center of a lens or mirror and is perpendicular to its surface.

Radius of Curvature (R)

: The radius of curvature is half the diameter of a sphere from which a curved mirror or lens is derived.

Ray Tracing

: Ray tracing is a method used to determine the path of light rays as they interact with mirrors and lenses. It involves drawing rays from an object and following their paths after reflection or refraction.

Spherical Mirrors

: Spherical mirrors refer to both concave and convex mirrors since they share the same shape - part of a sphere. These types of mirrors have curved surfaces that reflect light according to their specific curvature.

Vertex (V)

: The vertex refers to either one of two points on an optical element such as a lens or mirror where the principal axis intersects with it. In lenses, there is one vertex for each surface; in mirrors, there is only one vertex.

Virtual image

: A virtual image is an optical illusion created by the apparent intersection of light rays that do not actually converge. It is formed when light rays diverge after reflecting or refracting, giving the impression that the image is located behind a mirror or lens.

6.5 Images from Lenses and Mirrors

10 min readjanuary 8, 2023

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

Images From Lenses and Mirrors

Let’s talk about mirrors, optical devices that form images by reflecting light. We’ve all looked into a mirror and seen images of our faces and nearby objects; in this section, we’re going to analyze those images mathematically.


Plane Mirrors

are flat mirrors, and they’re the simplest type of mirror. Now, how is an image of an object in a mirror even formed? Well, light that’s reflected off of the object hits the mirror and reflects back into our eyes. The direction of the reflected rays determine where we perceive the image of the object to be.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-YXue9Oa4Ua0b.png?alt=media&token=e4f8ad79-7bd2-47cc-a116-c6049ff1e20e

Taken from Wikimedia Commons

We’re going to dive into the image characteristics of by answering the following questions:

1. Where’s the image, and how does the height of it compare with the object’s?

2. Is the image real or virtual?

3. Is the image upright or inverted?

(1) Think back to when you look at yourself in a flat mirror; it seems as if the image of yourself is behind the mirror. When you take a step sideways, the image of you also steps sideways. The image seems as far behind the mirror as the object is in front of the mirror(the can be used to show this). In a flat mirror, the image isn’t enlarged or shrunken compared to the size of the object.

(2) First off, what does it mean for an image to be real or virtual? An image is real if the light rays actually focus at the image; the light converges and passes through the actual image location. For flat mirrors, the image is virtual: light rays don’t actually pass through the image location on the other side of the mirror.

(3) Once again, re-imagine looking at yourself in a flat mirror. Your image isn’t upside down; it’s upright. Question 3 answered.

Check out this interactive to really solidify your understanding of .


Concave Mirrors & Convex Mirrors

Concave and are , mirrors that are specifically curved so that their surfaces form part of a sphere.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-aR7aEfVlvhli.png?alt=media&token=5dbbe5c4-91ae-45d4-a016-0a7582a0b904

Taken from Wikimedia Commons

  • The line that passes through the center of the surface and the center of curvature of a spherical mirror.
  • Center of Curvature (C)—The center of the imaginary sphere from which the section of the mirror was cut from.
  • Radius of Curvature (R)—The radius of the imaginary sphere.
  • Focal Point (Focus)—The point halfway between the center of curvature and mirror.
  • Focal Length (f)—The distance from the mirror to the focal point.
  • Vertex (V)—The intersection of the with the mirror; it’s also the geometric center of the mirror.

The focal length is one-half of the the radius of curvature:

f=R/2

The image above was a concave mirror; the reflective side is caved in towards the center of curvature. The following image is a convex mirror; the reflective side curves away from the center of curvature.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-kcplQQpG44Zj.png?alt=media&token=9508e4e6-4381-4124-8989-04f6abb8f210

Taken from Wikimedia Commons


Ray Tracing for Mirrors

is an essential tool that helps us determine the location of the image. We draw representative light rays in a diagram along with the object and the mirror: the point at which the reflected rays intersect is the location of the image. Let’s go over some of the rules:

Here are the steps for for mirrors:

  1. Draw a diagram showing the position of the mirror and the location of the object.
  2. Draw two rays emanating from the top and bottom of the object and reflecting off the mirror.
  3. Predict the path of the rays after they reflect off the mirror using the laws of reflection.
  4. Determine the location of the image by finding the intersection of the two rays.
  5. Determine the size and orientation of the image by comparing the object and the image.

:

  • An incident ray parallel to the is reflected through the focus.
  • An incident ray that travels through the focus is reflected parallel to the .
  • An incident ray that goes through the vertex is reflected at an equal angle to the .
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-9TNcbTX3yea5.png?alt=media&token=9bb45e57-7d52-43e1-b941-40b2b20d2f2f

Taken from Wikimedia Commons

:

  • An incident ray parallel to the is reflected in a way such that its extension passes through the focus.
  • An incident ray that travels through the focus is reflected parallel to the .
  • An incident ray that goes through the vertex is reflected at an equal angle to the .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-zEthWEYZ2i4a.png?alt=media&token=183886b7-714e-4ebe-b0da-6bfe63698b80

Taken from Wikimedia Commons

With , if the image is on the same side of the mirror as the object, then the image is real; if it’s formed on the opposite side, it’s virtual. Other aspects of the image (its size, location, orientation) can be also determined by . It might be a little tricky at first, but with practice, it'll get easier.


To answer our questions about images in an easier and faster way, we can use two equations. The first is the :

1/f=1/d_o+1/d_i

  • d_o​: the object’s distance from the mirror
  • d_i​: the image’s distance from the mirror

To differentiate mathematically between concave and convex, we set the focal length to the following:

  • For , f is positive value
  • For , f is negative value

The second equation is the :

M=-d_i/d_o=h_i/h_o

h_i​: height of image

h_o​: height of object

  • If d_i​ positive, then M is positive: the image is upright.
  • If d_i​ negative, then M is negative: the image is inverted.
  • If M<1, the image is reduced.
  • If M>1, the image is enlarged.
  • If M=1, the image is the same size as the object.

Keep in mind that all real images are inverted and all virtual images are upright.


Converging Lenses & Diverging Lenses

Lenses are optical devices that form images by refracting light. There are 2 types of lenses: converging and diverging.

Converging (convex) lens—converges parallel light rays to a focal point on the far side.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-jYe7GdgVeUET.png?alt=media&token=23b2e366-2dd7-40e6-bc59-e72e8fef1092

Taken from Wikimedia Commons

Diverging (concave) lens—causes light rays to diverge away from a focal point on the same side as the incident rays.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Rp7XhR39ZJvz.png?alt=media&token=b1ef94fd-1374-4645-9a2c-2a2398423c4b

Taken from Wikimedia Commons


Ray Tracing for Lenses

Just as we did with mirrors, we can use with lenses to get information about an image. Let’s go over the rules for for lenses:

Here are the steps for for lenses:

  1. Draw a diagram showing the position of the lens and the location of the object.
  2. Draw three rays emanating from the top, middle, and bottom of the object.
  3. Draw the first ray parallel to the optical axis and predict its path after it passes through the lens using the lens equation.
  4. Draw the second ray through the center of the lens and predict its path after it passes through the lens using the lens equation.
  5. Draw the third ray through the focal point of the lens and predict its path after it passes through the lens using the lens equation.
  6. Determine the location of the image by finding the intersection of the three rays.
  7. Determine the size and orientation of the image by comparing the object and the image.

Convex Lenses:

  • An incident ray traveling parallel to the is refracted through the focus.
  • An incident ray passing through the focus refracts through the lens and travels parallel to the .
  • Incident rays that travel through the center point of the lens pass undeflected.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-yKjqXDDDn1hX.png?alt=media&token=f892df27-3c3a-41dd-894f-dc053a180f99

Taken from Wikimedia Commons

Concave Lenses:

  • An incident ray traveling parallel to the axis refracts through the lens and travels in line with the focal point.
  • An incident ray passing through the focal point refracts through the lens and travels parallel to the .
  • Incident rays that travel through the center point of the lens pass undeflected.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-0iAKm2eHnJuJ.png?alt=media&token=84b8e0aa-43ce-4087-bc5e-36256c9ab2dc

Taken from Wikimedia Commons


The Equations of Lenses

Lens and mirrors use the same equations! Just keep in mind that:

  • Converging optical devices(+f): and convex lenses
  • Diverging optical devices(-f): and concave lenses

Some simulations to check out for lenses and mirrors:

Optics Bench Interactive

Concave Mirror Image Formation

Convex Mirror Image Formation

Converging Lens Image Formation

Diverging Lens Image Formation


Practice Problems

1. A plane mirror produces an image that is:

A) real, inverted, and larger than the object.

B) real, upright, and the same size of the object.

C) real, upright, and smaller than the object.

D) virtual, inverted, and smaller than the object.

E) virtual, upright, and the same size as the object.

2. An object is located 0.20 meters from a converging lens which has a focal length of 0.15 meters. Relative to the object, the image formed by the lens will be:

A) real, erect, smaller

B) real, inverted, smaller

C) real, inverted, larger

D) virtual, erect, larger

E) virtual, inverted, smaller

3. A narrow beam of monochromatic light enters a lens parallel to the optic axis, as shown in the accompanying diagram. Which arrow best represents the direction of the light after leaving the lens?

A) A

B) B

C) C

D) D

E) E

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-rwVUO1eYpnU3.png?alt=media&token=249480cc-0ba6-4f1d-a6b9-8c63c6f34e75

4. A beam of light traveling in glass (n_gng​ = 1.5) strikes a boundary with air (n_ana​ = 1.0) at point P. The angle of incidence is 60° as shown in the diagram. Which ray would best indicate the beam’s path after point P?

A) A

B) B

C) C

D) D

E) E

5. An object is placed 10 cm in front of the center of a concave curved mirror with a radius of curvature of 10 cm. About how far from the mirror will the real image of the object be formed?

A) 0 cm

B) 5 cm

C) 10 cm

D) 20 cm

E) No image is formed

6. A diverging lens produces an image of a real object. This image is

A) virtual, larger than the object, and upright

B) virtual, smaller than the object, and upright

C) virtual, smaller than the object, and inverted

D) real, smaller than the object, and inverted

7. An illuminated object is placed 0.30 meter from a lens whose focal length is –0.15 meter. The image is

A) inverted, real, and 0.30 meter from the lens on the opposite side from the object

B) upright, virtual, and 0.30 meter from the lens on the opposite side from the object

C) upright, real, and 0.10 meter from the lens on the same side as the object

D) upright, virtual, and 0.10 meter from the lens on the same side as the object

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Vl1wN18obp6h.png?alt=media&token=caf589d4-61e4-40b8-a661-dbd34648504c

Use the Figure above for questions 8 and 9. An object O is located at point P to the left of a converging lens, as shown in the figure. F_1F1​ and F_2F2​ are the focal points of the lens.

8. If the focal length of the lens is 0.40 m and point P is 0.30 m to the left of the lens, where is the image of the object located?

A) 1.2 m to the left of the lens B) 0.17 m to the left of the lens C) At the lens D) 0.17 m to the right of the lens E) 1.2 m to the right of the lens

9. Which of the following characterizes the image when the object is in the position shown?

A) Real, inverted, and smaller than the object B) Real, upright, and larger than the object C) Real, inverted, and larger than the object D) Virtual, upright, and larger than the object E) Virtual, upright, and smaller than the object

10. A physics student places an object 6.0 cm from a converging lens of focal length 9.0 cm. What is the magnitude of the magnification of the image produced?

A) 0.6

B) 1.5

C) 2.0

D) 3.0

E) 3.6


Answers:

  1. E: always makes virtual, same size, upright images

  2. C: Using the math, 1/f = 1/do + 1/di, and M = – di / do … di +0.6 M = – 3 …

  3. E: A horizontal beam approaching a converging lens bends and converges through the focal point

  4. E: Generally when we go from more–less we should always check the critical angle first rather than assuming the ray will refract and bend away. Choice D might be correct, but not until we first check the critical angle for total internal reflection. Use ni sin θc = nr sin (90), ni=1.5, nr=1θc = 41.8°. Since our incoming angle (60) is larger than the critical angle, total internal reflection will occur and you will get choice E.

  5. C: The focal point is = R/2. Then use the math 1/f = 1/do + 1/di … and di = 10

  6. E: Fact about diverging lens.

  7. D: Using the math, 1/f = 1/do + 1/di, and M = – di / do … di = – 0.10 m, M = +0.33

  8. A: Using the math, 1/f = 1/do + 1/di, di = –1.2. Its virtual so its on the same side as the object, which puts the image on the left side of the lens

  9. D: This is a magnifying glass, which can be memorized or the math can be done to prove the answer

  10. D: Using the math, 1/f = 1/do + 1/di, di = –18 … then M = – di / do … M = 3


Key Terms to Review (19)

Center of Curvature (C)

: The center of curvature is the center point of a sphere from which a curved mirror or lens is derived.

Concave lens

: A concave lens is a lens that is thinner in the middle and thicker at the edges, causing light rays to diverge when passing through it.

Concave Mirrors

: Concave mirrors are mirrors that curve inward, causing light rays to converge at a focal point. They are often used in telescopes and makeup mirrors.

Converging Lenses

: Converging lenses are lenses that are thicker in the middle and cause parallel light rays to converge or come together at a focal point after passing through the lens.

Convex lens

: A convex lens is thicker in the middle than at its edges and converges parallel rays of light that pass through it, bringing them together at a focal point.

Convex Mirrors

: Convex mirrors are mirrors that curve outward, causing light rays to diverge. They have a wider field of view but produce smaller images compared to concave mirrors. They are commonly used in car side-view mirrors.

Diverging Lenses

: Diverging lenses are lenses that are thinner in the middle and cause parallel light rays to spread out or diverge after passing through the lens.

Focal Length (f)

: The focal length is the distance between the center of a lens or mirror and its focal point. It determines how much a lens bends light and affects image formation.

Focal Point (Focus)

: The focal point, also known as the focus, is the point on the principal axis where parallel rays of light converge or appear to diverge from after passing through a lens or reflecting off a mirror.

Law of reflection

: The law of reflection states that the angle of incidence (the incoming angle) is equal to the angle of reflection (the outgoing angle) when light reflects off a surface.

Magnification Equation

: The magnification equation is an equation that relates the height of an image to the height of the object. It helps determine whether an image is magnified or reduced in size.

Mirror equation

: The mirror equation is a mathematical relationship that relates the object distance (distance of an object from a mirror), the image distance (distance of the image from the mirror), and the focal length of a mirror.

Plane Mirrors

: Plane mirrors are flat, smooth surfaces that reflect light in a predictable way. When light rays hit a plane mirror, they bounce off at the same angle they hit the mirror.

Principal Axis

: The principal axis is an imaginary line that passes through the center of a lens or mirror and is perpendicular to its surface.

Radius of Curvature (R)

: The radius of curvature is half the diameter of a sphere from which a curved mirror or lens is derived.

Ray Tracing

: Ray tracing is a method used to determine the path of light rays as they interact with mirrors and lenses. It involves drawing rays from an object and following their paths after reflection or refraction.

Spherical Mirrors

: Spherical mirrors refer to both concave and convex mirrors since they share the same shape - part of a sphere. These types of mirrors have curved surfaces that reflect light according to their specific curvature.

Vertex (V)

: The vertex refers to either one of two points on an optical element such as a lens or mirror where the principal axis intersects with it. In lenses, there is one vertex for each surface; in mirrors, there is only one vertex.

Virtual image

: A virtual image is an optical illusion created by the apparent intersection of light rays that do not actually converge. It is formed when light rays diverge after reflecting or refracting, giving the impression that the image is located behind a mirror or lens.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.