Answer:
The angle between the red and blue light is 1.7°.
Explanation:
Given that,
Wavelength of red = 656 nm
Wavelength of blue = 486 nm
Angle = 37°
Suppose we need to find the angle between the red and blue light as it leaves the prism
[tex]n_{r}=1.572[/tex]
[tex]n_{b}=1.587[/tex]
We need to calculate the angle for red wavelength
Using Snell's law,
[tex]n_{r}\sin\theta_{i}=n_{a}\sin\theta_{r}[/tex]
Put the value into the formula
[tex]1.572\sin37=1\times\sin\theta_{r}[/tex]
[tex]\theta_{r}=\sin^{-1}(\dfrac{1.572\sin37}{1})[/tex]
[tex]\theta_{r}=71.0^{\circ}[/tex]
We need to calculate the angle for blue wavelength
Using Snell's law,
[tex]n_{b}\sin\theta_{i}=n_{a}\sin\theta_{b}[/tex]
Put the value into the formula
[tex]1.587\sin37=1\times\sin\theta_{b}[/tex]
[tex]\theta_{b}=\sin^{-1}(\dfrac{1.587\sin37}{1})[/tex]
[tex]\theta_{b}=72.7^{\circ}[/tex]
We need to calculate the angle between the red and blue light
Using formula of angle
[tex]\Delta \theta=\theta_{b}-\theta_{r}[/tex]
Put the value into the formula
[tex]\Delta \theta=72.7-71.0[/tex]
[tex]\Delta \theta=1.7^{\circ}[/tex]
Hence, The angle between the red and blue light is 1.7°.
