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Question

Find the coordinates of image of point object P in mm formed after two successive reflections one at concave mirror and the other at convex.


A
(+30 cm, 14 mm)
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B
(+30 cm, 7 mm)
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C
(+20 cm, 16 mm)
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D
(+20 cm, 14 mm)
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Solution

The correct option is A (+30 cm, 14 mm)
Reflection at concave mirror (M1):

Object distance, u1=20 cm
Focal distance, f1=15 cm

Using mirror formula, 1v1+1u1=1f1 We get,

1v1=115+120

1v1=5300

v1=60 cm

Magnification:

m1=v1u1

m1=(60)20

m1=3

Since, initially the height of the point P is h=2 mm, so the height at which the image point will be

h=|m1|×h

h=3×2

h=6 mm


Reflection at convex mirror (M2):
The image formed by concave mirror acts as an object for convex mirror. So,

object distance, u2=(+6050)=+10 cm

Focal length, f2 = +20 cm

Using mirror formula:

1u2=1f21v2

1u2=120110

1u2=120

v2=20 cm

Hence, the final position of image after two successive reflection at concave mirror and then at convex 20 cm in front of convex mirror, M2.

Magnification:

m2=v2u2=(20)10=2

So, the image of the point will be formed above = m2 × (62)

=2×(8) mm

=16 mm principal axis of m2


So, the coordinate point of the final image will be
((50+v2) cm,(16+2) mm)

=((5020) cm,14 mm)

=(30 cm,14 mm)

Hence, option (a) is the correct answer.
Why this question:
To understand the image formation by combination of spherical mirrors.


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