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Chapter 18: Problem 59

For a material, the refractive indices for red, violet, and yellow colour light are, respectively, \(1.52,1.64\), and 1.60. The dispersive power of the material is (A) 2 (B) \(0.45\) (C) \(0.2\) (D) \(0.045\)

Short Answer

Expert verified
The dispersive power of the material is calculated using the formula \(\omega = \frac{n_v - n_r}{n_y - 1}\), where \(n_v\), \(n_r\), and \(n_y\) are the refractive indices for violet, red, and yellow light, respectively. Given the refractive indices as 1.64, 1.52, and 1.60, respectively, we find the dispersive power as \(\omega = \frac{1.64 - 1.52}{1.60 - 1} = \frac{0.12}{0.6} = 0.2\). Thus, the correct answer is (C) 0.2.

Step by step solution

01

Understand the Formula for Dispersive Power

Dispersive power is a measure of the ability of a medium to separate different wavelengths (colors) of light. It depends on the variation in refractive indices for different colors. The formula for dispersive power is given by: \[ 蠅 = \frac{n_v - n_r}{n_y - 1} \] Where, 蠅 is the dispersive power \(n_v\) is the refractive index of violet light \(n_r\) is the refractive index of red light \(n_y\) is the refractive index of yellow light Now, we have the values of the refractive indices for red, violet, and yellow light. Let's plug these values into the formula to find the dispersive power.
02

Calculate the Dispersive Power

Given the refractive indices for red, violet, and yellow light as 1.52, 1.64, and 1.60 respectively. Substituting these values into the formula, we get: \[ 蠅 = \frac{1.64 - 1.52}{1.60 - 1} \] Now calculate the numerator and denominator: \[ 蠅 = \frac{0.12}{0.6} \]
03

Find the Final Answer

Next, divide the numerator by the denominator to get the dispersive power: \[ 蠅 = \frac{0.12}{0.6} = 0.2 \] So, the dispersive power of the material is 0.2. Therefore, the correct option is (C) 0.2.

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