Question 1

A concave mirror has a focal length of 20 cm.What is the position (in cm)of the object if the image is upright and is two times larger than the object?
A)30
B)20
C)10
D)40
E)60

Accepted Answer

According to the magnification formula:
m=-v/u=-2 (as the image is 2 times larger than the object and is upright)
f=20cm
Using the mirror formula:
1/f=1/v+1/u
Plugging in the values,
1/20=1/v-1/u
We get
u=-15cm
Thus, the object is 15 cm in front of the mirror.

Question 2

An object 15 cm high is placed 15 cm in front of a convex mirror with a focal length of-10 cm.What is the image height (in cm)?
A)2
B)4
C)6
D)8
E)30

Accepted Answer

Using the mirror formula: 
1/f = 1/s + 1/s'
1/10 = 1/15 + 1/s'
Solving for s' we get s' = 30cm
Now using the magnification formula: 
m = -s'/s = -30/15 = -2
Since the magnification is negative, the image is inverted. 
|m| = h'/h 
2 = h'/15 
h' = 30cm 
Therefore, the image height is 30cm.

Question 3

A convex mirror has a focal length of-20 cm.What is the object distance if the image distance is -10 cm?
A)10 cm
B)40 cm
C)60 cm
D)20 cm
E)30 cm

Accepted Answer

D

Question 4

If you stand closer to a concave mirror than a distance of one focal length,the image you see is
A)real and inverted.
B)real and upright.
C)virtual and inverted.
D)virtual and upright.
E)none of the above because you do not get an image.

Accepted Answer

When standing closer than one focal length to a concave mirror, the image seen is virtual and upright. This is because the reflected light rays do not actually converge to form a real image, but instead appear to diverge from a virtual image point behind the mirror.

Question 5

A concave mirror has a focal length of 20 cm.What is the position (in cm)of the resulting image if the image is inverted and four times smaller than the object?
A)15
B)25
C)50
D)100
E)-15

Accepted Answer

Using the mirror formula, 1/f = 1/u + 1/v where f is the focal length, u is the object distance and v is the image distance.
We know that f = 20 cm and the image is inverted, so v is negative.
Let the object distance be x.
Using the magnification formula, m = -v/u = 1/4
-4v = u
Putting this value of u in the mirror formula, we get:
1/20 = 1/x - 1/4v
1/20 = (4v-x)/4vx
v = 5x/3
Substituting this value of v in the magnification formula,
-1/4 = -5x/3u
u = 15x/4
Therefore, the object distance is 15x/4 and the image distance is 5x/3.
Since the image is inverted, the image distance is negative, giving us -5x/3.
So, the position of the resulting image is 25 cm behind the mirror. Therefore, the answer is B.

Question 6

A dentist uses a concave mirror (focal length 2 cm)to examine some teeth.If the distance from the object to the mirror is 1 cm,what is the magnification of the tooth?
A)6
B)1
C)4
D)2
E)1.5

Accepted Answer

We can use the magnification formula:

magnification = -image distance/object distance

Since the image is virtual and upright, the magnification will be negative.

Using the mirror equation:

1/f = 1/di + 1/do

where f is the focal length, di is the image distance and do is the object distance, we can find the image distance:

1/2 = 1/di + 1/1

di = 2/3 cm

Plugging this into the magnification formula:

magnification = -(2/3)/1 = -2/3

Rounding to one significant figure, the magnification is -0.6, which is approximately -1. Therefore, the tooth appears to be the same size as the actual size when viewed through the mirror, so the magnification is 1.

Therefore, the answer is D) 2.

Question 7

Bottles of perfume sometimes have thick glass (n = 1.5)walls which give the impression the volume is larger than it really is.Assume a cylindrical bottle with an inner radius of 1.0 cm and an outer radius of 2.0 cm.What percentage of the apparent volume is the real volume?
A)95%
B)60%
C)80%
D)64%
E)75%

Accepted Answer

The apparent volume includes the volume of the glass walls, while the real volume only includes the volume of the perfume. The difference between the two volumes is the volume of the glass walls. 
The real volume can be calculated as: V_real = πr^2h, where r = 1.0 cm and h is the height of the cylinder. 
The apparent volume can be calculated as: V_apparent = π(R^2 - r^2)h, where R = 2.0 cm is the outer radius of the glass walls. 
The volume of the glass walls is: V_glass = V_apparent - V_real = π(R^2 - r^2)h - πr^2h = πh(3R^2 - 4r^2). 
The percentage of the apparent volume that the real volume represents is: V_real/V_apparent x 100% = (πr^2h) / (π(R^2 - r^2)h) x 100% = r^2 / (R^2 - r^2) x 100%. Plugging in the values, we get:

V_real/V_apparent x 100% = 1.0^2 / (2.0^2 - 1.0^2) x 100% = 0.64 x 100% = 64%

Therefore, the answer is D.

Question 8

An object is placed 10 cm in front of a concave mirror with a 20-cm focal length.Determine the image location (in cm).
A)-20
B)-15
C)-10
D)-5
E)6.7

Accepted Answer

The correct answer is A because the image location can be calculated using the thin lens equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. In this case, f = -20 cm (concave mirror), do = 10 cm, so di = -15 cm.

Question 9

A clown 2 m tall looks at himself in a full-length mirror (floor-to-ceiling).Where in the mirror must he look to see his feet?
A)1 m from the floor
B)50 cm from the floor
C)25 cm from the floor
D)at the bottom of the mirror
E)1.5 m from the floor

Accepted Answer

The clown must look at a point 1 m from the floor in the mirror to see his feet. This is because the angle of incidence equals the angle of reflection. The light reflecting from his feet to his eyes halfway up the mirror (1 m) makes the same angle with the normal (an imaginary line perpendicular to the mirror surface) as the light traveling from his feet to the mirror. Thus, he doesn't need to look at the bottom of the mirror to see his feet.

Question 10

A convex mirror has a focal length of -20 cm.What is the position of the resulting image (in cm)if the image is upright and four times smaller than the object?
A)-100
B)-25
C)-50
D)-15
E)-10

Accepted Answer

The answer of A convex mirror has a focal length...

Question 11

A concave mirror has a focal length of 20 cm.What is the magnification if the object and image distances are 10 cm and -20 cm respectively?
A)1
B)2
C)1/2
D)1/4
E)-1/2

Accepted Answer

The magnification (m) is given by the formula m = - (image distance) / (object distance). Here, the image distance is 20 cm and the object distance is 10 cm, so m = - (20 cm) / (10 cm) = -2. The negative sign indicates that the image is inverted.

Question 12

A concave mirror has a radius of curvature of 1.0 m.An object is placed 2.0 m in front of the mirror.Determine the location of the image (in cm).
A)130
B)83
C)67
D)150
E)200

Accepted Answer

Since the object is beyond the focal point, a real, inverted image is formed. Using the mirror equation, 1/f = 1/do + 1/di, where f is the focal length of the mirror, do is the distance of the object from the mirror, and di is the distance of the image from the mirror, we can solve for di. Plugging in the given values, we get 1/1 = 1/2 + 1/di, which simplifies to di = 0.67 m or 67 cm. Therefore, the answer is (C) 67.

Question 13

A magician can make a candle look as if it is burning under water by focusing light from a candle flame burning in air directly on top of an underwater candle.To do this you want to use a (Hint: eliminate those that cannot work. )
A)concave mirror farther than one focal length from the burning candle.
B)a convex mirror farther than one focal length from the burning candle.
C)a biconcave lens farther than one focal length from the burning candle.
D)a concave mirror closer than one focal length to the burning candle.
E)a convex lens closer than one focal length to the burning candle.

Accepted Answer

The answer of A magician can make a candle look...

Question 14

Bottles of perfume sometimes have thick glass (n = 1.5)walls which give the impression the volume is larger than it is.Assume a cylindrical bottle has an inner radius of 1.0 cm and an outer radius of 2.0 cm.How thick (in cm)would the wall appear if you could see a mark on the inside surface?
A)0.80
B)0.51
C)0.72
D)80
E)12

Accepted Answer

The apparent depth can be calculated using the formula $d' = \frac{d}{n}$, where $d$ is the actual depth and $n$ is the refractive index. The actual thickness of the glass is $2.0 \, \text{cm} - 1.0 \, \text{cm} = 1.0 \, \text{cm}$. Using the refractive index $n = 1.5$, the apparent thickness is $d' = \frac{1.0 \, \text{cm}}{1.5} = 0.67 \, \text{cm}$. However, given the options provided and the context of the question, it seems there was a mistake in my calculation. The correct approach to find the apparent thickness should involve considering how light bends when entering a denser medium from a less dense one, but without the exact formula or method provided in the options, the correct answer based on standard optical principles seems to be misaligned with the options given. Reevaluating the approach for calculating the apparent depth considering the refractive index and the geometry of the situation should yield a result that aligns with the options provided, indicating a mistake in the initial explanation.

Question 15

An object 4 cm high is placed 15 cm in front of a convex mirror with a focal length of-10 cm.What is the image position (in cm)?
A)-8
B)-4
C)-2
D)-6
E)30

Accepted Answer

The answer of An object 4 cm high is placed...

Question 16

The image of an object beneath the surface of a medium of refractive index n > 1 is seen in air by a person looking down on the surface.This image,formed by light rays leaving the flat refractive surface,is
A)real and closer to the viewer than the object.
B)virtual and closer to the viewer than the object.
C)real and farther from the viewer than the object.
D)virtual and farther from the viewer than the object.
E)virtual and the same distance from the viewer as the object.

Accepted Answer

When light passes from a denser to a rarer medium, the light refracts away from the normal. In this case, light travels from a medium with refractive index n (denser) to air (rarer). Therefore, the image formed by the light rays leaving the surface of the medium is virtual and closer to the viewer than the object.

Question 17

A concave mirror has a focal length of 20 cm.What is the magnification if the object's distance is 100 cm?
A)1/2
B)1/4
C)-2
D)4
E)-1/4

Accepted Answer

The answer of A concave mirror has a focal length...

Question 18

The inhabitants of a planet in another galaxy have their eyes at the exact center of their 4.0-m long bodies.How long must a plane mirror be for such a creature to be able to see all of its body in the mirror?
A)1.0 m
B)2.0 m
C)2.5 m
D)4.0 m
E)8.0 m

Accepted Answer

The answer of The inhabitants of a planet in another...

Question 19

When you stand in front of a convex mirror,the image you see is
A)real and inverted.
B)real and upright.
C)virtual and inverted.
D)virtual and upright.
E)real and inverted if your distance from the mirror is greater than two focal lengths.

Accepted Answer

When you stand in front of a convex mirror, the image you see is virtual and upright. This is because the rays of light that reflect off the convex mirror diverge, rather than converge, creating an image that appears smaller and closer than it actually is. This image is also upright, or right-side up, because the light rays do not cross over each other as they do with a concave mirror.

Question 20

An object is placed 15 cm in front of a concave mirror with a focal length of 30 cm.What is the magnification?
A)1
B)2
C)1/2
D)1/4
E)-2

Accepted Answer

The magnification (m) is given by the formula m = - (image distance/object distance). Using the mirror formula (1/f = 1/v + 1/u), where f = -30 cm and u = -15 cm, we find v = -30 cm. Thus, m = -(-30/-15) = 2.

Quiz 26: Image Formation by Mirrors and Lenses

A concave mirror has a focal length of 20 cm.What is the position (in cm) of the object if the image is upright and is two times larger than the object?

An object 15 cm high is placed 15 cm in front of a convex mirror with a focal length of-10 cm.What is the image height (in cm) ?

A convex mirror has a focal length of-20 cm.What is the object distance if the image distance is -10 cm?

If you stand closer to a concave mirror than a distance of one focal length,the image you see is

A concave mirror has a focal length of 20 cm.What is the position (in cm) of the resulting image if the image is inverted and four times smaller than the object?

A dentist uses a concave mirror (focal length 2 cm) to examine some teeth.If the distance from the object to the mirror is 1 cm,what is the magnification of the tooth?

Bottles of perfume sometimes have thick glass (n = 1.5) walls which give the impression the volume is larger than it really is.Assume a cylindrical bottle with an inner radius of 1.0 cm and an outer radius of 2.0 cm.What percentage of the apparent volume is the real volume?

An object is placed 10 cm in front of a concave mirror with a 20-cm focal length.Determine the image location (in cm) .

A clown 2 m tall looks at himself in a full-length mirror (floor-to-ceiling) .Where in the mirror must he look to see his feet?

A convex mirror has a focal length of -20 cm.What is the position of the resulting image (in cm) if the image is upright and four times smaller than the object?

A concave mirror has a focal length of 20 cm.What is the magnification if the object and image distances are 10 cm and -20 cm respectively?

A concave mirror has a radius of curvature of 1.0 m.An object is placed 2.0 m in front of the mirror.Determine the location of the image (in cm) .

A magician can make a candle look as if it is burning under water by focusing light from a candle flame burning in air directly on top of an underwater candle.To do this you want to use a (Hint: eliminate those that cannot work. )

Bottles of perfume sometimes have thick glass (n = 1.5) walls which give the impression the volume is larger than it is.Assume a cylindrical bottle has an inner radius of 1.0 cm and an outer radius of 2.0 cm.How thick (in cm) would the wall appear if you could see a mark on the inside surface?

An object 4 cm high is placed 15 cm in front of a convex mirror with a focal length of-10 cm.What is the image position (in cm) ?

The image of an object beneath the surface of a medium of refractive index n > 1 is seen in air by a person looking down on the surface.This image,formed by light rays leaving the flat refractive surface,is

A concave mirror has a focal length of 20 cm.What is the magnification if the object's distance is 100 cm?

The inhabitants of a planet in another galaxy have their eyes at the exact center of their 4.0-m long bodies.How long must a plane mirror be for such a creature to be able to see all of its body in the mirror?

When you stand in front of a convex mirror,the image you see is

An object is placed 15 cm in front of a concave mirror with a focal length of 30 cm.What is the magnification?