Question

23.
An object is situated at a distance of 15
cm from a convex mirror of focal length
30 cm. The position of the image formed
by it will be-
(1) – 5 cm
(2) 10 cm
(3) - 10 cm
(4) + 5 cm​

Answer 1

Answer :

• Image distance of the mirror is 30 cm.

Explanation :

Given :

• Object distance, u = 15 cm
• Focal length of the mirror, f = 30 cm

To find :

• Image distance, v = ?

Knowledge required :

Mirror formula :

$\boxed{\sf{\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}}}$

Where :

• f = Focal length of the mirror.
• v = Image distance
• u Object distance

Solution :

By using the mirror formula and substituting the values in it, we get :

$:\implies \sf{\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}} \\ \\ \\ :\implies \sf{\dfrac{1}{(-30)} = \dfrac{1}{v} + \dfrac{1}{(-15)}} \\ \\ \\ :\implies \sf{-\dfrac{1}{30} = \dfrac{1}{v} - \dfrac{1}{15}} \\ \\ \\ :\implies \sf{-\dfrac{1}{30} + \dfrac{1}{15} = \dfrac{1}{v}} \\ \\ \\ :\implies \sf{\dfrac{(-1) + 2}{30} = \dfrac{1}{v}} \\ \\ \\ :\implies \sf{\dfrac{1}{30} = \dfrac{1}{v}} \\ \\ \\ :\implies \sf{v = 30} \\ \\ \\ \boxed{\therefore \sf{v = 30}}$

Hence the image distance of the mirror is 30 cm.