Question

A marginal ray falls upon a concave mirror of radius of curvature 20 cm as shown in figure. Find distance CM (in cm).
​

Answer 1

Given,

A marginal ray falls upon a concave mirror of radius of curvature 20 cm as shown in figure.

To find,

The distance CM (see figure) in centimetre.

C is the centre of curvature. let P is the pole of concave mirror. so, CP = radius of curvature = 20cm

here, ∠i = ∠r = 30°

as aperture of mirror is very small.

so, CP = CT = 20cm [ see figure ]

see attached figure,

now applying sine rule,

CT/sin120° = CM/sin30°

⇒20cm/sin(180° - 60°) = CM/(1/2)

⇒20cm/sin60° = 2CM

⇒20cm/(√3/2) = 2 CM

⇒CM = 20/√3 cm

Therefore the distance CM is 20/√3 cm

also read similar questions : At what distance will the rays coming from the object at infinity converge in a concave mirror of radius of curvature 40...

https://brainly.in/question/1118807

an object is placed at centre of curvature of a concave mirror whose radius of curvature is 20 cm. the image is formed f...

https://brainly.in/question/1730128

Answer 2

Distance CM = 11.55 cm.

Explanation:

Given: A marginal ray falls upon a concave mirror. Radius of curvature = 20.

Find: Distance CM.

Solution:

P is the pole and C is the center of curvature of the concave mirror.

So radius of curvature = CP = 20cm (given)

We know that ∠i = ∠r = 30°

Hence CP = CT = 20cm

From the sine rule, we get:

CT / sin120° = CM / sin30°

20 / sin(180° - 60°) = CM / (1/2)

20 / sin60° = CM (1/2)

20 / (√3/2) = CM (1/2)

20 / √3 = CM

Therefore, distance CM = 11.55 cm.