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Chapter 5: Q2E (page 1105)

The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina. What are the ranges of (a) the wavelength, (b) the frequency, and (c) the speed of the light just as it approaches the retina within the vitreous humor?

Short Answer

Expert verified
  1. The range of the wavelength is from 284 nm to 560 nm .
  2. The range of the frequency is from 4.00脳1014Hzto 7.89脳1014Hz.
  3. The speed of the light as it approaches the retina is 2.24脳108m/s.

Step by step solution

01

(a) Determination of wavelength.

The speed changes, so the wavelength also changes accordingly.

The refractive index n = 1.34 . So the shift in wavelength is,

For vitreous humour,

位v=位0,vn=380nm1.34=284nm

For retina,

位v=位0,rn=750nm1.34=560nm

Thus, the range of wavelength is from 284 nm to 560 nm

02

(b) Determination of the frequency.

The frequency expression is,

f=v位

The frequency in air with v=c=3脳108m/s,

fr=c位r=3.00脳108m/s750脳10-9m=4.00脳1014Hz

The frequency for vitreous humour,

fr=c位v=3.00脳108m/s750脳10-9m=7.89脳1014Hz

Thus, the frequency ranges from 4.00脳1014Hzto 7.89脳1014Hz.

03

(c) Determination of the speed of light as it approaches the retina.

The expression for the speed is,

v=cn

Substitute all the values in the above equation,

v=3.00脳108m/s1.34=2.24脳108m/s

Thus, the speed with which light reaches the retina is2.24脳108m/s

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