Question

Part A

How far from a 53.0-mm-focal-length lens must an object be placed if its image is to be magnified 1.50× and be real?

Express your answer to three significant figures and include the appropriate units.

Part B

How far from a 53.0-mm-focal-length lens must an object be placed if its image is to be magnified 1.50× and be virtual?

Express your answer to three significant figures and include the appropriate units.

Answer 1

Magnification is given by:
M = -v/u
While lens equation is given by:
1/f = 1/u + 1/v
f = focal length of lens = -53.0 mm
u = object distance & v = image distance

Part A.)

When |M| = 1.50 and image is real, then
M = 1.50 = -v/u
v = -1.50*u
So,
1/f = 1/u + 1/v = 1/u - 1/(1.50*u)
1/f = 0.50/(1.50*u)
u = 0.50*f/1.50
Since f = -53.0 mm, So
u = 0.50*(-53.0)/1.50

u = -17.7 mm
Part B.)
Given that |M| = 1.50 & image is virtual, So
M = -1.50 = -v/u
v = 1.50*u
So,
1/f = 1/u + 1/v = 1/u + 1/(1.50*u)
1/f = 2.50/(1.50*u)
u = 2.50*f/(1.50)
Since f = -53.0 mm, So
u = 2.50*(-53.0)/1.50

u = -88.3 mm

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