Question

Where should a 3 cm tall object be placed in front of a concave mirror of radius 20 cm so that its image is real and 2 cm tall?

a. At 30 cm in front of the mirror
b. At 10 cm in front of the mirror
c. At 20 cm in front of the mirror
d. At 40 cm in front of the mirror

Answer 1

The 3 cm tall object should be placed 60 cm in front of the concave mirror to obtain a real and 2 cm tall image.

Step-by-step explanation:

To determine where the 3 cm tall object should be placed in front of a concave mirror of radius 20 cm so that its image is real and 2 cm tall, we can use the mirror formula:

1/f = 1/v - 1/u

where f is the focal length of the mirror, v is the image distance, and u is the object distance.

By substituting the given values into the formula, we can solve for u:

1/f = 1/v - 1/u

1/20 = 1/v - 1/30

1/20 = (30 - v)/30v

Simplifying the equation gives:

2v - 3v + 60 = 0

v = 60 cm

Therefore, the 3 cm tall object should be placed 60 cm in front of the mirror to obtain a real and 2 cm tall image.