Physics Class 12 NCERT Solutions: Chapter 10 Wave Optics Part 4

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Huygen's principle and double slit experiment

Huygen's Principle and Double Slit Experiment

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Q: 12. Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

Answer:

No; Wave theory

Newton’s corpuscular theory of light states that when light corpuscles strike the interface of two media from a rarer (air) to a denser (water) medium, the particles experience forces of attraction normal to the surface. Hence, the normal component of velocity increases while the component along the surface remains unchanged.

Hence, we can write the expression:

Where,

We have the relation for relative refractive index of water with respect to air as:

Hence, equation (i) reduces to

But,

Hence, it can be inferred from equation (ii) that. This is not possible since this prediction is opposite to the experimental results of.

The wave picture of light is consistent with the experimental results.

Q: 13. You have learnt in the text how Huygens’ Principle leads to the laws of reflection and refraction. Use the same principle to deduce directly that a point object placed in front of a plane mirror produces a virtual image whose distance from the mirror is equal to the object distance from the mirror.

Answer:

Let an object at O be placed in front of a plane mirror at a distance (as shown in the given figure).

Q 13 Object placed in front of mirror

Q 13 Object Placed in Front of Mirror

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A circle is drawn from the centre (O) such that it just touches the plane mirror at point O’. According to Huygens’ Principle, XY is the wavefront of incident light.

If the mirror is absent, then a similar wavefront X’Y’ (as XY) would form behind O’ at distance r (as shown in the given figure).

Q 13 Wavefront without mirror

Q 13 Wavefront Without Mirror

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X’Y’ can be considered as a virtual reflected ray for the plane mirror. Hence, a point object placed in front of the plane mirror produces a virtual image whose distance from the mirror is equal to the object distance (r).

Q: 14. Let us list some of the factors, which could possibly influence the speed of wave propagation:

(i) Nature of the source.

(ii) Direction of propagation.

(iii) Motion of the source and/or observer.

(iv) Wave length.

(v) Intensity of the wave. On which of these factors, if any, does

(A) The speed of light in vacuum,

(B) The speed of light in a medium (say, glass or water), depend?

Answer:

(A) The speed of light in a vacuum i.e., (approximately) is a universal constant. It is not affected by the motion of the source, the observer, or both. Hence, the given factor does not affect the speed of light in a vacuum.

(B) Out of the listed factors, the speed of light in a medium depends on the wavelength of light in that medium.

Q: 15. For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest; observer moving, and (ii) source moving; observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

Answer:

No Sound waves can propagate only through a medium. The two given situations are not scientifically identical because the motion of an observer relative to a medium is different in the two situations. Hence, the Doppler formulas for the two situations cannot be the same.

In case of light waves, sound can travel in a vacuum. In a vacuum, the above two cases are identical because the speed of light is independent of the motion of the observer and the motion of the source. When light travels in a medium, the above two cases are not identical because the speed of light depends on the wavelength of the medium.