Question

A concave lens has a focal length of $20cm$. An object $5cm$ tall is placed such that it forms an image at $15cm$ from the lens. Which of the following statements is/are true out of the following?

• A. Object is placed $60cm$ from the lens.
• B. Object is placed $30cm$ from the lens.
• C. Height of image is $1.25cm$
• D. Height of image is $2.25cm$

Answer 1

Answer: (A), (C)

The correct options are
A Object is placed $60cm$ from the lens.
C Height of image is $1.25cm$

Given:
Focal length of concave lens, $f=-20cm$
Height of the object, $h_o=5cm$
Image distance, $v=-15cm$

Let $u$ be the object distance and $h_i$ be the height of the image.

Using lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{-20}=\frac{1}{-15}-\frac{1}{u}$
$u=-60cm$
Object is placed $60cm$ from the lens.

From the formula of Magnification,
$m=\frac{h_i}{h_o}=\frac{v}{u}$
$⟹\frac{h_i}{5}=\frac{-15}{-60}$
$h_i=1.25cm$
Height of image is $1.25cm$.