Item 12 Part A Calculate Vred, the speed of red light in the diamond. To four si

Question

Item 12 Part A Calculate Vred, the speed of red light in the diamond. To four significant figures c= 2.998 × 108 m/s A beam of white light is incident on the surface of a diamond at an angle a. (Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. The indices of refraction in diamond are ned = 2.410 for red light and rblue = 2.450 for blue light. The surrounding air has nair 1.000. Note that the angles in the figure are not to scale Express your answer in meters per second to four significant digits Vred m/s Submit My Answers Give Up Part B Calculate Vblue, the speed of blue light in the diamond. To four significant figures c= 2.998 × 108 m/s Express your answer in meters per second to four significant digits Figure 1 of 1 bl m/s Submit My Answers Give Up 7 Part C red Derive a formula for , the angle between the red and blue refracted rays in the diamond Ghlu Express the angle in terms of Tred, Tblue, and a. Use nair-1. Remember that the proper way to enter the inverse sine of r in this case is asin(x) Hints

Explanation / Answer

a)  c = 2.998 * 10^8m/s.

The speed of light in a medium is:

c = (2.998 * 10^8) * (1.00 / nmedium)

For red light in diamond:

c = (2.998 * 10^8) * (1.00 / 2.410)
c = 1.244*10^8 m/s

b)

Just solve like in Part A. For blue light in diamond, n = 2.450.

c = (2.998 * 10^8) * (1.00 / 2.450)
c = 1.224*10^8 m/s

c)

Start with Snell’s law:

nair * sin(1) = ndiamond * sin(2)

For red light, the above becomes:

sin(1) = nred * sin(2, red)
2, red = asin(sin(1) / nred)

And for blue light:

sin(1) = nblue * sin(2, blue)
2, blue = asin(sin(1) / nblue)

Since we want the difference between the angles:

= asin(sin(1) / nred) – asin(sin(1) / nblue)

= asin(sin(1) / nred) – asin(sin(1) / nblue)

Calculate numerically for a = 45°.

Just use the formula

= asin(sin(1) / nred) – asin(sin(1) / nblue)
= asin(sin(45°) / 2.410) – asin(sin(45°) / 2.450)
= 16.7751° – 17.0619
= 0.2868°

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