Question

106- The focal length of a convex mirror is f. When an object is placed at a distance of 2f from it, the image distance is
(A) 2f
(B) f/2
(C) 2f/3
(D)f/3

Answer 1

Given :

In convex mirror,

Focal length : f

Object distance : 2f

To find :

The image distance.

Solution :

Using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

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

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

By substituting all the given values in the formula,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 2f} = \dfrac{1}{f}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{2f} = \dfrac{1}{f}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{f} + \dfrac{1}{2f}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{2 + 1}{2f}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{3}{2f}$

$\dashrightarrow\sf v = \dfrac{2f}{3}$

Thus, the image distance is 2f/3.

Answer 2

Hola ⚘⚘

• Given: In convex mirror, focal length = f; object distance = 2f.
• Need to find: distance of the image

Calculation:

>> 1/v + 1/u = 1/f

where,

• v = image distance
• u = object distance
• f = focal length

>> 1/v + 1/-2f = 1/f

>> 1/v - 1/2f = 1/f

>> 1/v = 1/f + 1/2f

>> 1/v = 2+1/2f

>> 1/v = 3/2f

>> v = 2f/3

Hence, the distance of the image is 2f/3

Option (c) is correct [✓]