A13 and A14 refer to two mirrors, 1 and 2. When an object is placed 10 cm from m

Question

A13 and A14 refer to two mirrors, 1 and 2. When an object is placed 10 cm from mirror 1, the image formed is virtual and 20 cm from the mirror. When the object is placed 20 cm from mirror 2, the image is virtual and 10 cm from the mirror. A13. (i) Which statement about the mirrors is true? Both mirrors must be convex Both mirrors must be concave Mirror 1 is convex and mirror 2 is concave Mirror 1 is concave and mirror 2 is convex Mirror 1 is a plane mirror and mirror 2 could be concave or convex Calculate the radius of curvature of the spherical surface of which mirror 1 is a part.

Explanation / Answer

A13(1) Correct answer is (D) Mirror 1 is concave and 2 is convex.

Because:

Given,

Let o be the object distance, i be the image distance.

o1 = 10 cm ; i = -20 cm (as its a virtual image)

o2 = 20 cm and i1 = -10 cm (again its a virtual image)

we know from lens equation that,

1/f = 1/i + 1/o

f = o x i / (o + i)

f1 = o1 x i1 / (o1 + i1) = 10 x -20 / (10 - 20) = +20 cm(concave)

f2 = o2 x i2 / (o2 + i2) = 20 x -10 / (20 - 10) = -20 cm(conved)

A13(1) Correct answer is (D) Mirror 1 is concave and 2 is convex.

(ii) The radius of curvature will be double of the focal length of the mirror.

So R1 = 2 x f1 = 2 x +20cm = 40 cm

Hence, R1 = 40 cm.

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