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Question

An object of size 50 cm is placed 20 cm in front of a spherical mirror and its image of size 25 cm is formed above the principal axis. Find the focal length as per sign convention and the type of spherical mirror used here?

A
25 cm, concave mirror
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B
20 cm, concave mirror
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C
+25 cm, convex mirror
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D
+20 cm, convex mirror
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Solution

The correct option is D +20 cm, convex mirror
Given,
Height of the image h=+25 cm (positive since image is formed above principal axis)
Height of the object (h)=50 cm
Object distance (u)=20 cm
Let M be the magnification produced, v be the image distance and f be the focal length of the mirror.

We know that,
M=vu=hh

vu=2550=12

v20=12

Image distance (v)=+10 cm
Positive sign indicates that image is formed right of the mirror.

Now applying mirror formula,

1v+1u=1f

110120=1f

1f=120

focal length,f=+20 cm
Since focal length is positive and the image is virtual and erect, the mirror must be convex.


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