An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 800

To a distant observer, the light appears to be coming from somewhere below the ground. The observer naturally assumes that light is being reflected from the ground, say, by a pool of water near the tall object. Such inverted images of distant tall objects cause an optical illusion to the observer. This phenomenon is called mirage. This type of mirage is especially common in hot deserts. Based on the above facts, answer the following questions:

(a) Which of the following phenomena is prominently involved in the formation of mirage in deserts?

(i) Refraction, Total internal Reflection 

(ii) Dispersion and Refraction

(iii) Dispersion and scattering of light 

(iv) Total internal Reflection and diffraction.

(b) A diver at a depth 12m inside water\(( a_{\mu_{ \omega}}=\dfrac{4}{3})\)  sees the sky in a cone of semi- vertical angle

(i) \( sin^{-1}\dfrac{4}{3}\)

(ii) \( tan^{-1}\dfrac{4}{3}\)

(iii) \( sin^{-1}\dfrac{3}{4}\)

(iv) 90°

(c) In an optical fibre, if n₁ and n₂ are the refractive indices of the core and cladding, then which among the following, would be a correct equation?

(i) n₁ < n₂ 

(ii) n₁ = n₂

(iii) n₁ << n₂ 

(iv) n₁ > n₂

(d) A diamond is immersed in such a liquid which has its refractive index with respect to air as greater than the refractive index of water with respect to air. Then the critical angle of diamond-liquid interface as compared to critical angle of diamond -water interface will

(i) depend on the nature of the liquid only 

(ii) decrease

(iii) remain the same 

(iv) increase.

(e) The following figure shows a cross-section of a ‘light pipe’ made of a glass fiber of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for the following phenomena to occur.

(i) 0 < i < 90° 

(ii) 0 < i < 60°

(iii) 0 < i < 45° 

(iv) 0 < i < 30°

(a) "If the slits in Young's double slit experiment are identical, then intensity at any point on the screen may vary between zero and four times to the intensity due to single slit". Justify the above statement through a relevant mathematical expression.

(b) Draw the intensity distribution as function of phase angle when diffraction of light takes place through coherently illuminated single slit.

Answer the following questions:-

(a) Name the e.m. waves which are suitable for radar systems used in aircraft navigation. Write the range of frequency of these waves.

(b) If the Earth did not have atmosphere, would its average surface temperature be higher or lower than what it is now? Explain.

(c) An e.m. wave exerts pressure on the surface on which it is incident. Justify.

The focal length of a convex lens made of glass of refractive index (1.5) is 20 cm. What will be its new focal length when placed in a medium of refractive index 1.25 ?
Is focal length positive or negative? What does it signify?

Light of wavelength 2000 Å falls on a metal surface of work function 4.2 eV.

(a) What is the kinetic energy (in eV) of the fastest electrons emitted from the surface?

(b) What will be the change in the energy of the emitted electrons if the intensity of light with same wavelength is doubled?

(c) If the same light falls on another surface of work function 6.5 eV, what will be the energy of emitted electrons?