Answer:
The angle at which the light emerges from the opposite face of the prism with respect to the original incident beam is 53.3°.
Explanation:
Given that,
Angle [tex]\theta=\dfrac{\pi}{4}[/tex]
[tex]\theta=45[/tex]
Refractive index n=1.5
For the refraction at the first surface
We need to calculate the angle
Using formula of refraction
[tex]n_{a}\sin\theta_{1}=n_{g}\sin\theta_{2}[/tex]
Put the value into the formula
[tex]1\sin\dfrac{\pi}{4}=1.5\sin\theta_{2}[/tex]
[tex]\sin\theta_{2}=\dfrac{1\times\sin45}{1.5}[/tex]
[tex]\sin\theta_{2}=0.46520[/tex]
[tex]\theta_{2}=\sin^{-1}(0.46520)[/tex]
[tex]\theta_{2}=27.7^{\circ}[/tex]
We need to calculate the angle on incidence at the second surface
[tex](90-\theta_{2})+(90-\theta_{3})+A=180[/tex]
[tex]\theta_{3}=A-\theta_{2}[/tex]
Put the value into the formula
[tex]\theta_{3}=60-27.7[/tex]
[tex]\theta_{3}=32.3[/tex]
For the refraction at the second surface,
We need to calculate the angle at which the light emerges from the opposite face of the prism with respect to the original incident beam direction
Using formula of refraction
[tex]n_{g}\sin\theta_{3}=n_{a}\sin\theta_{4}[/tex]
Put the value into the formula
[tex]1.5\sin32.3=1\times\sin\theta_{4}[/tex]
[tex]\theta=\sin^{-1}(\dfrac{1.5\sin32.3}{1})[/tex]
[tex]\theta=53.3^{\circ}[/tex]
The angle is 53.3° from the original
Hence, The angle at which the light emerges from the opposite face of the prism with respect to the original incident beam is 53.3°.
Answer:
[tex]r'=36.0113^{\circ}[/tex]
Explanation:
Given:
Form the Snell's law we know:
[tex]n=\frac{sin\ i}{sin\ r}[/tex] ...................(1)
where:
[tex]r=[/tex] angle of refraction when light passes from air to glass.
putting values in (1)
[tex]1.5=\frac{sin\ 45^{\circ}}{sin\ r}[/tex]
[tex]r= 28.125^{\circ}[/tex]
Now refer the schematic for further geometric relations involved:
From the triangle LMN:
[tex]r+i'=90^{\circ}[/tex]
[tex]i'=61.875^{\circ}[/tex] is the second angle of incidence when the light ray incidents on glass-air interface when passing from glass to air.
Again using Snell's law:
[tex]1.5=\frac{sin\ 61.875^{\circ}}{sin\ r'}[/tex]
[tex]r'=36.0113^{\circ}[/tex] which is the angle of emergence.
