Respuesta :
Answer:
The angle of dispersion between the two refracted rays in the oil is 0.51°.
Explanation:
Given that,
Wavelength in vacuum
[tex]\lambda_{1}= 450\ nm[/tex]
[tex]\lambda_{2}=650\ nm[/tex]
The indices of refraction is
[tex]n_{1}=1.440[/tex]
[tex]n_{2}=1.420[/tex]
We need to calculate the refracted angle for 450 wavelength
Using Snell's law
[tex]\dfrac{\sin\theta_{1}}{\sin\theta_{2}}=\dfrac{n_{2}}{n_{1}}[/tex]
[tex]\sin\theta_{2}=\dfrac{n_{1}\sin\theta_{1}}{n_{2}}[/tex]
[tex]\theta_{2}=\sin^{-1}(\dfrac{n_{1}\sin\theta_{1}}{n_{2}})[/tex]
Put the value into the formula
[tex]\theta_{2}=\sin^{-1}(\dfrac{1\times\sin50}{1.440})[/tex]
[tex]\theta_{2}=32.13^{\circ}[/tex]
We need to calculate the refracted angle for 650 wavelength
Using Snell's law
[tex]\dfrac{\sin\theta_{1}}{\sin\theta_{2}}=\dfrac{n_{2}}{n_{1}}[/tex]
[tex]\theta_{2}=\sin^{-1}(\dfrac{n_{1}\sin\theta_{1}}{n_{2}})[/tex]
Put the value into the formula
[tex]\theta_{2}'=\sin^{-1}(\dfrac{1\times\sin50}{1.420})[/tex]
[tex]\theta_{2}'=32.64^{\circ}[/tex]
We need to calculate the angle of dispersion between the two refracted rays in the oil is
[tex]\theta=\theta_{2}'-\theta_{2}[/tex]
Put the value into the formula
[tex]\theta=32.64-32.13[/tex]
[tex]\theta=0.51^{\circ}[/tex]
Hence, The angle of dispersion between the two refracted rays in the oil is 0.51°.
