8 and 9 please Light with a wavelength of 589 nm in a vacuum strikes the surface

Question

8 and 9 please

Light with a wavelength of 589 nm in a vacuum strikes the surface of an unknown liquid at an angle of 31.2 degree with respect to the normal to the surface. If the light travels at a speed of 1.97 times 10^8 m/s through the liquid, what is the angle of refraction? a) 19.9 degree b) 26.1 degree c) 34.2 degree d) 39.3 degree c) 51.9 degree A beam of light that consists of a mixture of red light (lambda = 660 nm in vacuum) and violet light (lambda = 410 nm in vacuum) falls on a grating that contains 1.0 times 10^4 lines/cm. Find the angular separation between the first-order maxima (m = 1) of the two wavelengths if the experiment takes place in a vacuum. a) 11 degree b) 17 degree c) 24 degree d) 41 degree c) 65 degree

Explanation / Answer

8. We know refractive index, n = c/v

where c-> velocity of light in vacumm = 3×108 m/sec

and v-> velocity of light in the liquid

Therefore, n = 3×108/1.97×108

   n = 1.52

Again by Snell's law,

n = sin i/sin r

1.52 = sin 58.8 0/sin r ( i =90-31.2= 58.80)

sin r = 0.8553/1.52 = 0.5702

So, r = 34.20     

Option is (c).   

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