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Question

# A container is filled with water (μ=1.33) upto a height of 33.25 cm. A convex mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level. Focal length of the mirror is

A
15cm
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B
20cm
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C
18.31cm
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D
10cm
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Solution

## The correct option is C −18.31cmThe image I′ for first refraction (i.e., when the ray comes out of liquid) is at a depth of =33.251.33=25 cm[∵Apparent depth=Real depthμ]Now, reflection will occur at concave mirror. For this I′ behaves as an object∴u=−(15+25)=−40 cm,f=f,v=?Using mirror formula1f=1v+1u=1v−140⇒v=40f40+f...(i)But v=−[15+251.33]...(ii)where 251.33 is the real depth of the image.From Eqs. (i) and (ii),40f40+f=−[15+251.33]=−33.79⇒f=−18.31 cm.

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