Problem 32.55 A ray of light with wavelength ? is incident from air at precisely

Question

Problem 32.55

A ray of light with wavelength ? is incident from air at precisely 60? ( = ?) on a spherical water drop of radius r and index of refraction n (which depends on ?). When the ray reemerges into the air from the far side of the drop, it has been deflected an angle ? from its original direction as shown in the figure.
(Figure 1)

Part A

By how much does the value of ? for violet light (n = 1.341) differ from the value for red light (n = 1.330)?

Express your answer using two signiifcant figures.

??=?violet??red= = ..............

??=?violet??red= = ..............

Explanation / Answer

For violet light

n1 sin theta1 = n2 sin theta2

sin theta2 = 1 * sin 60 / 1.341

theta2 = 40.23 deg

delta theta = 60 - 40.23 = 19.77 deg

delta thetanet = 2 * 19.77 = 39.54 deg

For red light

n1 sin theta1 = n2 sin theta2

sin theta2 = 1 * sin 60 / 1.330

theta2 = 40.63 deg

delta theta = 60 - 40.63 = 19.37 deg

delta thetanet = 2 * 19.37 = 38.74 deg

difference = 39.54 - 38.74

= 0.80

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