### Chapter 1: Light - Reflection and Refraction

Q
##### Light - Reflection and Reflection

Question:

A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Here, the given lens is concave.

Focal length ($f$) = -15 cm

Image distance ($v$) = -10 cm

Object distance ($u$) = ?

Image distance ($v$) is taken negative because the concave lens forms the image on the same side of the lens.

And, focal length ($f$) is taken negative because the lens is concave.

Using the lens formula,

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

$\frac{1}{-15} = \frac{1}{-10}-\frac{1}{u}$

$\frac{1}{-15} +\frac{1}{10} = -\frac{1}{u}$

$\frac{1}{15} -\frac{1}{10} = \frac{1}{u}$

$\frac{1}{u} = \frac{2-3}{30}$

$\frac{1}{u} = \frac{-1}{30}$

$u = -30 cm$

The negative value of u shows that the object is placed in front of the lens at a distance of 30 cm from the optical centre.

Ray diagram for the given concave lens:

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