Question

An object of size 3 cm is placed at a distance 27 cm from pole of a concave mirror which produce a real image 6 cm high

A. what is focal length of the mirror ?
B. Find the position of the mirror.

Answer 1

Solution:

Given:

=> Height of the object (h) = 3 cm

=> Object distance (u) = -27 cm

=> Height of the image (h') = 6 cm.

To Find:

=> Focal length of the mirror.

=> Position of mirror (v).

Formula used:

$\sf{\implies \dfrac{h'}{h}=-\dfrac{v}{u}}$

$\sf{\implies \dfrac{1}{f} =\dfrac{1}{v} +\dfrac{1}{u}\;\;\;\;(Mirror\;Formula)}$

So, firstly we will find position of mirror (v),

$\sf{\implies \dfrac{h'}{h}=-\dfrac{v}{u}}$

$\sf{\implies \dfrac{6}{3}=-\dfrac{v}{(-27)}}$

${\boxed{\boxed{\sf{\implies v=54\;cm}}}}$

Now, we will find focal length of image by mirror formula,

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

$\sf{\implies \dfrac{1}{f} =\dfrac{1}{54}+\dfrac{1}{(-27)}}$

$\sf{\implies \dfrac{1}{f} = \dfrac{1-2}{54}}$

$\sf{\implies \dfrac{1}{f} = -\dfrac{1}{54}}$

${\boxed{\boxed{\sf{\implies f=-54\;cm}}}}$

So, Focal length of the mirror = -54 cm

Position of mirror = 54 cm.

Answer 2

Refer the attachment.

Or

$\huge\bf{Answer:-}$

• 3cm is the height of object.
• -27 is the object's distance.
• 6cm is the height of image.

Accoding to the given question:-

• We have to find the what is focal length of the mirror and also find the position of the mirror.

Using Formula

$\bf=> h/h = (-) v/u$

$\bf=> 1/f = 1/v + 1/u$

This the the mirror formula

So,

$\bf=> h/h = (-) v/u$

$\bf=> 6/3 = (-) v/-27$

.•. V => 54 cm

Now let us finf the length of image by using the mirror formula.

$\bf=> 1/t = 1/v + 1/u$

$\bf=> 1/f = 1/54 + 1/-27$

$\bf=> 1/f = (1-2)/54$

$\bf=> 1/f = (-) 1/54$

Therefore , focal length = -5cm

• Hence,(-54 cm ) is the focal length.

And

• (54 is the position of the mirror).