Optics 2 Question 30

29. A parallel beam of light travelling in water (refractive index =4/3 ) is refracted by a spherical air bubble of radius 2mm situated in water. Assuming the light rays to be paraxial.

(1988,6M)

(a) Find the position of the image due to refraction at the first surface and the position of the final image.

(b) Draw a ray diagram showing the positions of both the images.

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Answer:

Correct Answer: 29. (a) 6mm,5mm

Solution:

  1. (a)

Applying μ2vμ1u=μ2μ1R, one by one on two spherical surfaces.

First on left surface

1v14/3=14/3+21v1=16v1=6mm

i.e. first image will be formed at 6mm towards left of P

Second on right surface Now, distance of first image I1 from Q will be 10mm (towards left).

4/3v2110=4/31243v2=16110=415v2=5mm

or

(b) The ray diagram is shown in figure.

NOTE

  • At P and Q both normal will pass through C.
  • At P ray of light is travelling from a denser medium (water) to rarer medium (air) therefore, ray of light will bend away from the normal and on extending meet at l1. Similarly at Q, ray of light bends towards the normal.
  • Both the images I1 and I2 are virtual.


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