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Define critical angle and calculate it for glass-air interface. Give two applications of total internal reflection.

Physics

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Answer

c

42.5∘42.5^\circ

Step-by-step solution

3 steps

Part b

The critical angle is the angle of incidence in the optically denser medium for which the angle of refraction in the optically rarer medium is 90∘90^\circ.

Part c

42.5∘42.5^\circ

  1. Identify the given values.

    The refractive index of glass, nglass=1.48n_{glass} = 1.48.
    The refractive index of air, nair=1.00n_{air} = 1.00.
    From the diagram, the ray is incident at point X on the glass-air interface. The refracted ray travels along the interface, meaning the angle of refraction in air is r=90∘r = 90^\circ. The angle 'i' is the angle of incidence in the glass.

  2. Apply Snell's Law for the critical angle.

    When light travels from a denser medium (glass) to a rarer medium (air) and the angle of refraction is 90∘90^\circ, the angle of incidence is the critical angle.
    Snell's Law: nglasssin⁡i=nairsin⁡rn_{glass} \sin i = n_{air} \sin r

  3. Substitute the values and solve for ii.

    1.48×sin⁡i=1.00×sin⁡90∘1.48 \times \sin i = 1.00 \times \sin 90^\circ

    Since sin⁡90∘=1\sin 90^\circ = 1:

    1.48×sin⁡i=1.00×11.48 \times \sin i = 1.00 \times 1 sin⁡i=1.001.48\sin i = \frac{1.00}{1.48} sin⁡i=0.67567\sin i = 0.67567 i=arcsin⁡(0.67567)i = \arcsin(0.67567) i=42.5∘i = 42.5^\circ

    Angle ii is 42.5∘\boxed{42.5^\circ}.

Part d

Two applications of total internal reflection are

  • Optical fibers for transmitting data (e.g., internet, medical imaging).
  • Periscopes and binoculars use prisms to reflect light without significant loss of intensity.
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