Question

A concave mirror of radius of curvature 20 cm forms
image of the sun. The diameter of the sun subtends
an angle 1° on the earth. Then the diameter of the
image is (in cm):
(1) 21/9
(3) 20
(2) I/9
(4) 1/18​

Answer 1

The diameter of image is $\dfrac{\pi}{18}$

(4) is correct option.

Explanation:

Given that.

Radius of curvature = 20 cm

Angle = 1°

As sun is more far from the earth,

Then we take u = infinite

We need to calculate the image distance

Using formula of mirror

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

$\dfrac{1}{-10}=\dfrac{1}{v}+\dfrac{1}{\infty}$

$v= -10\ cm$

We need to calculate the diameter of image

Using formula of angle subtends

$\theta=\dfrac{d}{f}$

$d=f\times\theta$

Put the value into the formula

$d=10\times\dfrac{\pi}{180}$

$d=\dfrac{\pi}{18}\ cm$

Hence, The diameter of image is $\dfrac{\pi}{18}$

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Topic : Diameter of image

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