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

 

Answers (1)

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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