Solution of Chapter 10. Wave Optics (Physics - Exemplar Book)

Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in Fig. 10.1. A Polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid.

Consider sunlight incident on a slit of width 10⁴ A. The image seen through the slit shall

Consider a ray of light incident from air onto a slab of glass (refractive index n) of width d, at an angle θ. The phase difference between the ray reflected by the top surface of the glass and the bottom surface is

In a Young’s double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case

Figure 10.2 shows a standard two slit arrangement with slits S₁, S₂. P₁, P₂ are the two minima points on either side of P (Fig. 10.2). At P₂ on the screen, there is a hole and behind P₂ is a second 2- slit arrangement with slits S₃, S₄ and a second screen behind them.

Two source S₁ and S₂ of intensity I₁ and I₂ are placed in front of a screen [Fig. 10.3 (a)]. The pattern of intensity distribution seen in the central portion is given by Fig. 10.3 (b). In this case which of the following statements are true.

Consider sunlight incident on a pinhole of 10³A. The image of the pinhole seen on a screen shall be

Consider the diffraction pattern for a small pinhole. As the size of the hole is increased

For light diverging from a point source

Is Huygens’s principle valid for longitudinal sound waves?

Consider a point at the focal point of a convergent lens. Another convergent lens of short focal length is placed on the other side. What is the nature of the wave fronts emerging from the final image?

What is the shape of the wave front on earth for sunlight?

Why is the diffraction of sound waves more evident in daily experience than that of light wave?

The human eye has an approximate angular resolution of ϕ = 5.8×10^–4 rad and a typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance z should a printed page be held so that one does not see the individual dots.

A polaroid (I) is placed in front of a monochromatic source. Another polaroid (II) is placed in front of this polaroid (I) and rotated till no light passes. A third polaroid (III) is now placed in between (I) and (II). In this case, will light emerge from (II). Explain.

Can reflection result in plane polarized light if the light is incident on the interface from the side with higher refractive index?

For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of and electrons accelerated through 100V used as the illuminating substance.

Consider a two slit interference arrangements (Fig. 10.4) such that the distance of the screen from the slits is half the distance between the slits. Obtain the value of D in terms of such that the first minima on the screen falls at a distance D from the centre O.

Figure 10.5 shown a two-slit arrangement with a source which emits unpolarised light. P is a polarizer with axis whose direction is not given. If I₀ is the intensity of the principal maxima when no polarizer is present, calculate in the present case, the intensity of the principal maxima as well as of the first minima.

A small transparent slab containing material of μ =1.5 is placed along AS₂ (Fig.10.6). What will be the distance from O of the principal maxima and of the first minima on either side of the principal maxima obtained in the absence of the glass slab.

AC = CO = D, S₁C = S₂C = d << D

Four identical monochromatic sources A, B, C, D as shown in the (Fig.10.7) produce waves of the same wavelength and are coherent. Two receiver R₁ and R₂ are at great but equal distances from B.

(i) Which of the two receivers picks up the larger signal?

(ii) Which of the two receivers picks up the larger signal when B is turned off?

(iii) Which of the two receivers picks up the larger signal when D is turned off?

(iv) Which of the two receivers can distinguish which of the sources B or D has been turned off?

The optical properties of a medium are governed by the relative permittivity (ε_r) and relative permeability (μ_r ). The refractive index is defined as For ordinary material ε_r > 0 and μ_r > 0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with ε_r < 0 and μ_r < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials As light enters a medium of such refractive index the phases travel away from the direction of propagation.

(i) According to the description above show that if rays of light enter such a medium from air (refractive index = 1) at an angle in 2nd quadrant, them the refracted beam is in the 3rd quadrant.

(ii) Prove that Snell’s law holds for such a medium.

To ensure almost 100 per cent transitivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF₂ (n = 1.38). What should the thickness of the film be so that at the center of the visible spectrum (5500 Å) there is maximum transmission.