Chapter 35: Q. 22 (page 1017)

A hydrogen discharge lamp emits light with two prominent wavelengths: $656 n m$ (red) and $486 n m$ (blue). The light enters
a flint-glass prism perpendicular to one face and then refracts
through the hypotenuse back into the air. The angle between
these two faces is $35 °$ .
a. Use Figure $35.18$ to estimate to $\pm 0.002$ the index of refraction
of flint glass at these two wavelengths.
b. What is the angle (in degrees) between the red and blue light
as it leaves the prism?

Expert verified

(a) The index of refraction of flint glass at these two wavelengths are $n_{R} = 1.572$ and $n_{B} = 1.587$

(b) The angle between the red and blue light as it leaves the prism $1.16 °$ .

Step by step solution

We need to estimate the index of refraction of flint glass at the two wavelengths.

$λ = 656 n m n_{R} = 1.572 λ = 486 n m n_{B} = 1.587$ .
Here $λ$ is the wavelength and $n$ is refractive index.

We need to find angle between the red and blue light.

$n_{1} \sin σ_{1} = n_{2} \sin σ_{2} σ_{2} = \sin^{- 1} (\frac{n_{1} \sin σ_{1}}{n_{2}})$

RED: BLUE:

$n_{1} = 1.572 n_{1} = 1.587 n_{2} = 1.00 n_{2} = 1.00 σ_{1} = 35 ° σ_{1} = 35 ° σ_{2} = 64.37 ° σ_{2} = 65.54 °$

$σ = σ_{B} - σ_{R} = 1.16 °$ .

Here $n$ is the refractive index and $σ$ refraction angle.

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