Question

An object is placed 30cm away from a concave mirror of radius of curvature 40cm. Find the position, nature size of image.​

Answer 1

Explanation:

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Answer 2

Given :

In concave mirror,

Object distance = - 30 cm

Radius of curvature = 40 cm

To find :

The position, size and nature of the image.

Solution :

we know that,

if f is the focal length of a mirror and R is its radius of curvature, then f = R/2

by substituting the given values in the formula,

$\dashrightarrow \sf f = \dfrac{R}{2}$

$\dashrightarrow \sf f = \dfrac{40}{2}$

$\dashrightarrow \sf f = 20$

Now, 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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 30} = \dfrac{1}{ - 20}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{30} = \dfrac{1}{ - 20}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{ - 20} + \dfrac{1}{30}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 3 + 2}{60}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 1}{60}$

$\dashrightarrow\sf v = - 60 \: cm$

Thus, the position of image is 60 cm

Nature of image :

• The image is formed in front of the concave mirror, it's nature will be real and inverted.