Reflection and refraction

1.What happens when light passes through the interface of two media?

Solution:

When light passes through the interface of two media from the first medium (where it moves with velocity v1) into the second medium (where it moves with velocity v2), two cases may occur:

  • reflection of light
  • refraction of light

Reflection of Light:

Reflection of light occurs when light strikes a medium into which it cannot penetrate.

Law of Reflection:
α=α′\alpha = \al 
The angle of reflection α′\alpequals the angle of incidence α. The reflected ray lies in the plane of incidence.

Total Internal Reflection – refraction of light from an optically denser medium into an optically less dense medium. (β=90∘\beta = 90^\circ)

sin⁡αm=1n1,n2=1,αm=critical angle\sin \alpha_m = \frac{1}{n_1}, \quad n_2 = 1, \quad \alpha_m = \text{critical angle}

Refraction of Light:

Refraction of light occurs when light passes into another medium.

Law of Refraction (Snell’s Law):

sin⁡αsin⁡β=v1v2=n2n1\frac{\sin \alpha}{\sin \beta} = \frac{v_1}{v_2} = \frac{n_2}{n_1}

  • α\alpha = angle of incidence,

  • β\beta = angle of refraction,

  • n1n_1 = refractive index of the first medium,

  • n2n_2 = refractive index of the second medium.

If β<α\beta < \alpha, the ray bends toward the normal.
If β>α, the ray bends away from the normal.

Absolute Refractive Index:

n=cv=cλf=λ0λn = \frac{c}{v} = \frac{c}{\lambda f} = \frac{\lambda_0}{\lambda}

Medium     Air     Water     Ice     Glass
nn     1.00     1.33     1.31     1.51

2.The speed of red light in glass is v1 = 199,200 km.s-1 and violet is v2 = 196,700 km.s-1. Determine the refractive index for red and violet light. (c = 3.108 m.s-1)

Solution:

Analysis:

physics-reflection-and-refraction-2.gif 

The refractive index for red light in glass is n1 = 1.507, for violet light it is n2 = 1.525.

3.Light falls from air (n1 = 1) onto the wall of a diamond at an angle α = 680. The refracted ray is perpendicular to the reflected ray. Calculate:

  • the refractive index of the diamond for the used light
  • the speed of light in the diamond (c = 3.108 m.s-1)

Solution:

Analysis:

physics-reflection-and-refraction-3.gif 

  • The refractive index of diamond is n2 = 2.475.
  • The speed of light in diamond is v = 1.212·108 m.s-1.

4.Light falling from air onto the surface of water (n = 1.33) is refracted at an angle β = 300. Determine the angle of incidence α and the angle of reflection α‘.

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5.At the bottom of a lake, a vertical post 1 meter long is planted so that it is completely submerged under the water surface. Determine the length of its shadow on the bottom of the lake if n1(air) = 1, n2(water) = 1.33, and the Sun is φ = 300 above the surface.

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6.A light ray falls from air onto a flat interface of air and glass, reflects at an angle of 600 and at the same time refracts into glass at an angle of 300. Determine the speed of light in glass.

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7.The wavelength of yellow light in air is λ0 = 590 nm. What will be the wavelength of light in glass if n = 1.5? Also calculate the speed of light in this medium.

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8.At what critical angle must light fall in order for total reflection to occur, if light passes:

  • a) from glass to air (n1 = 1.5)
  • b) from water to air (n‘1 = 1.33)
  • c) from glass to water n2(air) = 1
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9. Determine the thickness of the soap bubble wall (n = 1.33) if white light falls on it. The first-order interference maximum is observed in green light (fZ = 5.7·1014 Hz).

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10.At the bottom of a stream 32 cm deep lies a pebble. A boy wants to touch it with a stick that he holds above the surface at an angle of 450. At what distance from the pebble will the stick touch the bottom of the stream after immersion? (n1=1, n2=1.33)

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11. The refractive index of ice is n1 = 1.31, of glass n2 = 1.51, of oil n3 = 1.47. What is the speed of light in these media?

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12. Calculate the refractive index of a material if for an angle of incidence α = 300 from air the angle of refraction is β = 150. What must the new angle of incidence α/ be if the angle of refraction is β/ = 21.50?

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13.A light ray falls on a plane mirror at an angle of incidence α = 200. How does the angle between the incident and reflected ray change if the ray falls on the mirror at an angle α/ = 350?

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14.A light ray passes from water (n1 = 1.33) into glass (n2 = 1.51). Decide whether it is refraction toward the normal or refraction away from the normal if the angle of incidence is α = 600.

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15. By how large an angle did a small mirror rotate if, on a scale located l = 150 cm from the mirror, the light beam shifts from the zero position—where it falls perpendicularly on the scale—by h = 25 cm?

odraz-a-lom-svetla-15-1
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16.A light ray falls on a mirror. The mirror rotates by 10 around an axis lying in the plane of the mirror and perpendicular to the ray. By what angle will the reflected ray deflect? By how much will the light spot shift on a screen perpendicular to the reflected ray and 5 m away from the mirror?

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17. What is the critical angle for light incident on the boundary between glass (n1 = 1.51) and water (n2 = 1.33)?

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18.At a depth h = 600 mm below the water surface, a point light source is placed. Determine the shape and size of the part of the water surface through which the light emerges above the surface.

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19.The refracted ray forms an angle ω = 900 with the reflected ray. Determine the relative refractive index of the material into which the ray refracts, if sin α = 0.8 holds.

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20. A light ray falls from air (n = 1) onto glass at an angle α = 600. The refractive index of glass for red light is n1 = 1.735, for violet n2 = 1.811. Determine the angle between the refracted red and violet rays.

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