- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# A magnifying lens has a focal length of 100 mm. An object whose size is 16 mm is placed at some distance from the lens so that an image is formed at a distance of 25 cm in front of the lens.**(a)** What is the distance between the object and the lens?**(b) **Where should the object be placed if the image is to form at infinity?

Focal length of the lens $f$ = 100 mm

Height of object, $h$ = 16 mm

Image distance, $v$ = $-$25 cm = $-$250 mm (negative because the image is virtual)

To find: Distance between the object and the lens, $u$.

Solution:

From the lens formula we know that-

$\frac {1}{v}-\frac{1}{u}=\frac{1}{f}$

Substituting the given values in the formula we get-

$\frac {1}{(-250)}-\frac{1}{u}=\frac{1}{100}$

$-\frac {1}{250}-\frac{1}{100}=\frac{1}{u}$

$\frac{1}{u}=\frac {-2-5}{500}$

$\frac{1}{u}=-\frac {7}{500}$

$u=-\frac {500}{7}$

$u=-71.4mm$

$u=-7.14cm$

Thus, the distance between the object and the lens is **7.14 cm.**

**(b) **The object should be placed at the focus $F'$ (here 100mm) so that the image is formed at infinity.

So, $u$= $-$100mm = $-$10 cm.

Thus, the object should be placed at **10 cm** in front of the lens.

__Image is posted for reference only__