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A ray of light, incident on an equilateral glass prism of refractive index √3, moves parallel to the base line of the prism inside it. Find the angle of incidence​

Respuesta :

ItzHeartRider

As the ray of light moves parallel to the base line of the prism inside it, so angle of refraction = r = 30° (equilateral prism)

Now, we know that:

[tex]{:\implies \quad \sf \sin (i)=\mu \sin (r)}[/tex]

[tex]{:\implies \quad \sf \sin (i)=\sqrt{3}\sin (30^{\degree})}[/tex]

[tex]{:\implies \quad \sf \sin (i)=\dfrac{\sqrt{3}}{2}}[/tex]

[tex]{:\implies \quad \sf \sin (i)=\sin (60^{\degree})}[/tex]

Therefore, angle of incidence is 60°

Xerxis

Given ,

[tex]r = \sqrt{3}[/tex]

Now ,

[tex] \longrightarrow \sin(i) = \sqrt{3} \: \sin(30°)[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow \sin(i)= \sqrt{ \frac{3}{2} }[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \longrightarrow \: i = 60°[/tex]

The angle of incidence is 60°.

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