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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is .

Answers (1)

 Given focal length of lents (f) = 1.5 cm  

Object distance u = - 20 cm ,  f = 15 cm

We know that \frac{1}{f}=\frac{1}{v}-\frac{1}{u}=\frac{1}{v}=\frac{1}{f}+\frac{1}{u}

\frac{1}{v}=\frac{1}{15}-\frac{1}{20}

\frac{1}{v}=\frac{4-3}{60}

v = 60 cm 

The image 1 gets formed at 60 cm to ghe right of the lens and it will be inverted.

Therefore, Distance between lens and mirror will be

d = image distance(v) - radius of curvature of convex mirror

s = 60 - 2f 

\Rightarrow    2f = 60 - 5

f=\frac{55}{2}=27.5\ cm(convex mirror) 

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