A concave spherical mirror with a focal length of 11 cm faces a plane mirror wit

Question

A concave spherical mirror with a focal length of 11 cm faces a plane mirror with the optical axis of the spherical mirror perpendicular to the plane mirror. A small object is placed at point P on the optical axis, 11 cm from the plane mirror and 34 cm from the vertex of the spherical mirror. Find the distance from the plane mirror to the three nearest images. (Enter your answers from smallest to largest.) The first nearest image is 11 cm and the second nearest image is 28.74 cm. How do you find what the third nearest image is and what is the answer?

Explanation / Answer

1st Image will be formed by plane mirror of object

distance of image will be as distance of object from plane mirror in opposite direction.

!st image = 11 cm

2nd :

image of object by concave mirror

1/f = 1/i + 1/o

1/11 = 1/i + 1/34

i = 16.26 cm from concave mirror.

distance from plane mirror = (11 + 34) - 16.26 = 28.74 cm

3rd Image :

image formed by concave mirror will behave like object for plane mirror.

so image formed by plane mirror of this image will be at 28.74 cm form mirror in opposite
direction.

so third image will also be at 28.74 cm

(If you want third nearest distance then image by plane mirror will behave as objecr for
concave mirror.)

o = 11 + 34 + 11 = 56 cm

1/11 = 1/i + 1/56

i = 13.69 cm from concave mirror.

distance from plane mirror = 11 + 34 - 13.69 = 31.31 cm )

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