Chapter 33: Q52P (page 1004)

In Fig.33-52a, a beam of light in material1is incident on a boundary at an angle of $θ_{1} = 30 °$ . The extent of refraction of the light into material2depends, in part, on the index of refraction $n_{2}$ of material 2. Fig.33-52bgives the angle of refraction $θ_{2}$ versus $n_{2}$ for a range of possible $n_{2}$ values. The vertical axis scale is set by $θ_{2 a} = 20 {.0}^{°}$ and $θ_{2 b} = 40 {.0}^{°}$
(a) What is the index of refraction of material 1?
(b) If the incident angle is changed to $60^{°}$ and material 2has $n_{2} = 2 .4$ , then what is angle $θ_{2}$ ?

Short Answer

Expert verified

The index of refraction of material 1 is $1.7$ .
The angle , if incident angle changed to $60^{0}$ and material 2 has $n_{2} = 2.4$ is $38^{\circ}$ .

Step by step solution

Given data

The angle of incidence at the boundary of material 1 is, $θ_{1} = 30^{\circ}$ .

Understanding the concept

We can use the formula of Snell’s law to each boundary to find the index of refraction of material 1and angle $θ_{2}$ ; if $θ_{1}$ is changed to $60^{\circ}$ and the index of the refraction of material 3 is2.4.

Formula:

$n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$

(a) Calculate The index of refraction of the material 1

According to Snell’s law,

$n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$

Therefore, $n_{1} = n_{2}$ if $θ_{1} = θ_{2}$ .

Since, $θ_{1} = 30^{\circ}$ , $θ_{2} = 30^{\circ}$

From figure33-52(b), we can conclude that,

$θ_{2} = 30^{\circ}$ is at $n_{2} = 1.7$

Therefore,

$n_{1} = 1.7$

Therefore, the index of the refraction of material 1 is $1.7$

(b) Calculate the angleθ2 ; if the incident angle changed to 60∘, and material 2 has n2=2.4

We have,

$n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$

For, $θ_{1} = 60^{\circ}$ and $n_{2} = 2.4$ ,

Then we can calculate the angle $θ_{2}$ as,

$\begin{matrix} θ_{2} = \sin^{- 1} (\frac{(1.7) \sin 60^{°}}{2.4}) \\ θ_{2} = {37.83}^{°} \\ ~ 38^{°} \end{matrix}$

Therefore, angle $θ_{2}$ , if the incident angle changed to $60^{\circ}$ and material 2 has $n_{2} = 2.4$ is $38^{°}$ .

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Short Answer

Step by step solution

Given data

Understanding the concept

(a) Calculate The index of refraction of the material 1

(b) Calculate the angleθ2 ; if the incident angle changed to 60∘, and material 2 has n2=2.4

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