# A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to :(Refractive index of water =1.33) Option 1) $13.4cm$ Option 2) $11.7cm$ Option 3) $6.7cm$ Option 4) $8.8cm$

As we can see first the image will be formed by mirror

$\Rightarrow \frac{1}{v}+\frac{1}{u}=\frac{1}{f}$                              $(f=-20cm)$

$\Rightarrow \frac{1}{v}+\frac{1}{-5}=\frac{1}{-20}$

$\Rightarrow v=\frac{20}{3}cm$

Refraction from water surface

$\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=0$

$\Rightarrow \frac{1}{v}-\frac{1.33}{-\frac{35}{3}}=0$

$\Rightarrow v=8.8cm$

Option 1)

$13.4cm$

Option 2)

$11.7cm$

Option 3)

$6.7cm$

Option 4)

$8.8cm$

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