Provide a brief justification for the answer you selected. (a) A mixture of blue

Question

Provide a brief justification for the answer you selected. (a) A mixture of blue light (wavelength of 400 nm) and red light (wavelength of 630 nm) tails on a (transmission) diffraction grating that contains 2 times 10^3 lines/cm. What is the angular separation of the two colors at the first-order maxima? Make a simple sketch to support your answer. A beam of light that consists of a mixture of red, green and violet light strikes a prism (surrounded by air) as shown. Indices of refraction for this prism tor the various colors are indicated in the table. An observer is located to the right of the prism as shown

Explanation / Answer

for all the rays incident angle, theta_i = 45 degrees

let us find critical angle for the given three rays.

for red color,

Apply Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

sin(theta_c)/sin(90) = 1/1.37 (since, when theta_i = theta_c , theta_r = 90 degrees)

sin(theta_c) = 0.73

theta_c = sin^-1(0.73)

= 46.88 degrees > 45 degrees

so, red color refracts and passes through the prism.

for green color,

Apply Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

sin(theta_c)/sin(90) = 1/1.4 (since, when theta_i = theta_c , theta_r = 90 degrees)

sin(theta_c) = 0.714

theta_c = sin^-1(0.714)

= 45.6 degrees > 45 degrees

so, green color refracts and passes through the prism.

for violet color,

Apply Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

sin(theta_c)/sin(90) = 1/1.43 (since, when theta_i = theta_c , theta_r = 90 degrees)

sin(theta_c) = 0.699

theta_c = sin^-1(0.714)

= 44.37 degrees < 45 degrees

so, for violet color total internal reflection takes place. it will not transmit through the prism.

so, the obsorver can see red and green color but not violet color.

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