A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface.  A small air bubble is 6 cm below the flat surface inside it along the axis.  The position of the image of the air bubble made by the mirror is seen :

 

  • Option 1)

    14 cm below flat surface

  • Option 2)

    30 cm below flat surface

  • Option 3)

    20 cm below flat surface

  • Option 4)

    16 cm below flat surface

 

Answers (1)
V Vakul

As we learnt in

Relation between focal length and radius of curvature -

f=\frac{R}{2}

 

- wherein

R = Radius of curvature

This is valid only for smaller angle of incidence.

i.e.paraxial rays

 

 

Mirror Formula -

\frac{1}{v}+\frac{1}{u}=\frac{1}{f}


 

- wherein

u= Object distance from pole of mirror.

v= Image distance from pole of mirror.

f= focal length of the mirror.

 

 

Relation between real depth and apparent depth -

\frac{n_{i}}{d}= \frac{n_{r}}{d{}'}

 

- wherein

n_{i} = Refractive index of medium of incident.

n_{r} = Refractive index of medium of refraction.

d = distance of object.

d{}' = apparent  depth

 

 Given radius of hemispherical glass R = 10 cm

\therefore   focla length f=\frac{10}{2}=-5\ cm

    u=(10-6)=-4\ cm

By using mirror formula

\frac{1}{v}+\frac{1}{u}=\frac{1}{f}=\frac{1}{v}+\frac{1}{-4}=\frac{1}{-5}\ \; \Rightarrow\ \; v = 20\ cm

Apparent height h_{a}=h_{r}\frac{\mu_{1}}{\mu_{2}}=30\times \frac{1}{1.5}=20\ cm

below flat surface.

Correct option is 3.

 

 

 


Option 1)

14 cm below flat surface

This is an incorrect option.

Option 2)

30 cm below flat surface

This is an incorrect option.

Option 3)

20 cm below flat surface

This is the correct option.

Option 4)

16 cm below flat surface

This is an incorrect option.

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