Figures 9.34(a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively.
Figures 9.34(a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence in water is 45º with the normal to a water-glass interface [Fig. 9.34(c)].
As per the given figure, for the glass − air interface:
Angle of incidence, i = 60°
Angle of refraction, r = 35°
The relative refractive index of glass with respect to air is given by Snell’s law as:
$\mu_{\mathrm{g}}^{\mathrm{a}}=\frac{\sin i}{\sin r}$
$=\frac{\sin 60^{\circ}}{\sin 35^{\circ}}=\frac{0.8660}{0.5736}=1.51$ ..(1)
As per the given figure, for the air − water interface:
Angle of incidence, i = 60°
Angle of refraction, r = 47°
The relative refractive index of water with respect to air is given by Snell’s law as:
$\mu_{\mathrm{w}}^{\mathrm{a}}=\frac{\sin i}{\sin r}$
$=\frac{\sin 60}{\sin 47}=\frac{0.8660}{0.7314}=1.184$ ...(2)
Using (1) and (2), the relative refractive index of glass with respect to water can be obtained as:
$\mu_{\mathrm{g}}^{\mathrm{w}}=\frac{\mu_{\mathrm{g}}^{\mathrm{a}}}{\mu_{\mathrm{w}}^{\mathrm{a}}}$
$=\frac{1.51}{1.184}=1.275$
The following figure shows the situation involving the glass − water interface.
Angle of incidence, i = 45°
Angle of refraction = r
From Snell’s law, r can be calculated as:
$\frac{\sin i}{\sin r}=\mu_{\mathrm{g}}^{\mathrm{w}}$
$\frac{\sin 45^{\circ}}{\sin r}=1.275$
$\sin r=\frac{\frac{1}{\sqrt{2}}}{1.275}=0.5546$
$\therefore r=\sin ^{-1}(0.5546)=38.68^{\circ}$
Hence, the angle of refraction at the water − glass interface is 38.68°.
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
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- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
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- Dual Nature of Matter
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- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
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