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Example questions based on refraction at plane surface

 

example questions:

1)    Why is it difficult to shoot a fish swimming in water?

ANS: this is because of refraction of light when it enters from water to air.

As it is entering from denser to rarer medium it bends away to normal. This refracted when it is extended back virtually, a virtual image of the fish is formed above the fish. This virtual image is seen by the observer but not the real fish. So experienced fishers will target just below the fish what they see. Observe the below figure.

Shooting fish in water

2)    The speed of the light in a diamond is 1, 24, 000 km/s. Find the refractive index of diamond if the speed of light in air is 3,00,000 km/s.

 

ANS: Let v be the speed of light in diamond=> v=1,24,000 km/s

                                                                                          Or 124000x103 m/s

Given speed of light in air (C) is 300000 km/s

ð 300000x103 m/s

We know µ=c/v

µ=300000x103 m/s÷124000x103 m/s

µ=300/124

=2.419 approximately

 

3)    Refractive index of glass relative to water is 9/8. What is the refractive index of water relative to glass?

ANS: given µ glass/µwater=9/8

Then µwater/µglass =8/9

 

4)    The absolute refractive index of water is 4/3. What is the critical angle?

ANS: Given µ=4/3

We know µ=1/sin c

Sin c=1/µ

Sin c=1/(4/3)

Sin c=3/4

C=sin -1(3/4)

=48.50

 

5)    i) A light ray is incident on air-liquid interface at 450and is refracted at 300. What is the refractive index of the liquid? ii) For what angle of incidence will the angle between reflected ray and refracted ray be 900?

ANS:

i)                   i=450

r=300

µ1=1(air)

by applying Snell’s law=>  µ1 sin(i)=µ2 sin(r)

1xsin450=µ2 sin300

ð µ2=(1/ root 2)/(1/2)

ð 2/ root 2

Root 2. Or 1.414.

Light reflection and refraction

ii) Given the angle between the reflected and refracted ray = 90°
It means angle of reflection (r1) + angle of incidence (i) = 90°
Angle of refraction (r) = (90° - i)
But refractive index n = sin i/ sin r

=sin i/sin(90-i)

=sin i/cos i  [∵sin(90-θ)=cos θ]
From Natural tangent tables tan 54.7° = 1.414 = tan i
The angle of incidence i = 54.7°

                                        

                                                         THANK YOU

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