Question

Question.
Rohit placed a pencil perpendicular to principal axis in front of a converging mirror of focal length 30 cm. The image formed is twice the size of the pencil. Calculate the distance of the object from the mirror.

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Answer 1

Given :

• The object = A and 'u'

• The Image = A' and 'v'

• Type of mirror = Converging (Concave)

• Focal Lenght = 30cm

Concept :

Given that the Image (A') is twice the Object(A) So, We Know that if the mirror is concave, The image formed is larger than object, if it is virtual . So, we can take (A') as (-v) . We will calculate the Magnification and The distance of object on the basis of this.

To Find :

• The distance of object from the mirror

Solution :

So, Object = A or u,

Image = A' or -v

Focal Lenght = 30cm

Now, As Given, The image is twice the length of Object, so :

A' = 2A

Magnification = Image/Object

$\implies \displaystyle \rm m = \frac{2a}{a}$

$\implies \displaystyle \rm \frac{ - v}{u} = \frac{2a}{a}$

$\implies \displaystyle \rm \frac{ - v}{u} = 2$

$\implies \displaystyle \rm - v = 2u$

$\implies \displaystyle \rm v - 2u$

So, As we got, Image distance = -(2×object distance)

So, using the formula:

$\implies \displaystyle \rm \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\implies \displaystyle \rm \frac{1}{ - 30} = \frac{1}{ - 2u} + \frac{1}{u}$

$\implies \displaystyle \rm \frac{ - 1}{2u} + \frac{1}{u} = \frac{1}{ - 30}$

$\implies \displaystyle \rm \frac{ - 1 + 2}{2u} = \frac{1}{ - 30}$

$\implies \displaystyle \rm \frac{2u}{1} = - 30$

$\implies \displaystyle \rm2u = - 30$

$\implies \displaystyle \rm u = \frac{ - 30}{2}$

$\red{ \underline{ \boxed{ \therefore \displaystyle \rm u = - 15cm}}}$

So, The pencil is placed at -15cm from the mirror

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Answer 2

Explanation:

Given :

• The object = A and 'u'

• The Image = A' and 'v'

• Type of mirror = Converging (Concave)

• Focal Lenght = 30cm

Solution :

So, Object = A or u,

Image = A' or -v

Focal Lenght = 30cm

Now, As Given, The image is twice the length of Object, so :

A' = 2A

⟹m= a 2a

⟹ u −v

= an 2a

2⟹ u − v =2

- v = 2u⟹−v=2u

v - 2u ⟹

So, using the formula :

U = 15 cm

So, The pencil is placed at

-15cm from the mirror ...

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