JIPMER2016PhysicsWave Optics
Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 Å . When the slit is illuminated by light of another wavelength, then the angular width decreases by 30 % . The same decrease in angular width of central maximum is obtained when the original apparatus is immersed in a liquid. The refractive index of the liquid will be
Options
- A1.25
- B1.42
- C1.67
- D1.5
Correct answer
B. 1.42
Step-by-step solution
Given, ₁=6000 Å , ₂=? Angular width of central maximum = 2 a ₁= 2 ₁ a ....(i) and ₂= 2 ₂ a ₂= ₁ 0.7 ₁ 0.7= 2 ₂ a .....(ii) From Eqs. (i) and (ii), we get aligned 1 0.7 & = ₁ ₂ ₂ & = ₁ 0.7=6000 0.7 & =4200 Å aligned when immersed in liquid, aligned ₂ & = ₁ ₂ & = ₁ 0.7 aligned 2 ₂ a = 2 ₁ a 0.7 [ ₂= ₁ ] aligned & 2 ₁ / a & = 2 ₁ a 0.7 & 1 & =0.7 =1.42 aligned