Question

An object is placed $50cm$ away from a spherical lens of radius of curvature $15cm$. As a result, an erect and diminished image is formed. Which of the following statements is/are CORRECT?

• A. Image distance = $-6.52cm$
• B. The lens is a concave lens.
• C. Image distance = $-8.45cm$
• D. The lens is a convex lens.

Answer 1

Answer: (A), (B)

The correct options are
A Image distance = $-6.52cm$
B The lens is a concave lens.

Given:
A spherical lens of radius of curvature, $R=15cm$
The object distance, $u=-50cm$ (Object distance is always negative, irrespective of the type of the lens.)
An erect and diminished image is formed, i.e. the image formed is virtual, erect and diminished in nature. Such an image can be formed only in a concave lens, because a convex lens cannot form virtual images that are diminished in nature.
The focal length of a concave lens is negative.
Focal length, $f=\frac{R}{2}=\frac{-15}{2}cm$
Using the mirror formula, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$⟹\frac{1}{\left(\frac{-15}{2}\right)}=\frac{1}{v}-\frac{1}{(-50)}$

$⟹\frac{-2}{15}=\frac{1}{v}+\frac{1}{50}$

$⟹\frac{1}{v}=\frac{-2}{15}-\frac{1}{50}=\frac{-23}{150}$

$⟹v=\frac{-150}{23}=-6.52cm$
$\therefore$ the image distance, $v=-6.52cm$