A diverging lens is placed in front of a plane mirror as in the diagram to the r

Question

A diverging lens is placed in front of a plane mirror as in the diagram to the right. The separation of the lens and the mirror exactly equals the magnitude of the lens’s focal length , which is -1.32m . An object is placed twice this distance (2.64m ) on the other side of the lens.

a. Find the position of the image seen by eye A (which is looking into the mirror). Express your answer as a distance measured from the mirror, and indicate which side of the mirror the image appears on (left or right).

b. Find the lateral magnification (relative to the original object) of the image seen by eye A . Indicate whether the image is upright or inverted.

Explanation / Answer

a)

for lens

object distance s1 = 2.64 m

focal length f = -1.32 m

image distance = s1' = ?

fromlens equation

1/s1 + 1/s1' = 1/f1

1/2.64 + 1/s1' = -1/1.32

s1' = -0.88 m

for the mirror

the image at s1' is the object

object distance for mirror

s2 = 0.88 + 1.32 = 2.2 m

for the mirror

the image distance is same as that of object s2' = 2.2 m

the image is at distance 2.2 from the mirror <<------------ANSWER

the image is to the right side of the mirror <<------------ANSWER

=====================

b)

magnification m = -s1'/s1 = 0.88/2.64 = 0.33 <<------------ANSWER

-------------------------

c)

for lens

object distance s1 = 2.64 m

focal length f = -1.32 m

image distance = s1' = ?

fromlens equation

1/s1 + 1/s1' = 1/f1

1/2.64 + 1/s1' = -1/1.32

s1' = -0.88 m

for the mirror

the image at s1' is the object

object distance for mirror

s2 = 0.88 + 1.32 = 2.2 m

for the mirror

the image distance is same as that of object s2' = 2.2 m

the image is at distance 2.2 from the mirror

this image will act as a object for lens once again

s3 = 2.2 + 1.32 = 2.52 m

1/s3 + 1/s3' = 1/f

1/2.52 + 1/s3' = -1/1.32

image distance s3' = 0.86625 m <<------------ANSWER

magnification m = m1*m3 = -(s1'/s1)*(-s3'/s3)

m = (0.88/2.46)*(0.86625/2.52)

m = 0.123 <<----ANSWER

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