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A ray of light incident at an angle thet...

A ray of light incident at an angle `theta` on a refracting face of a prism emerges from the other face normally. If the angle of the prism is `5^@` and the prism is made of a material of refractive index `1.5`, the angle of incidence is.

A

`7.5^(@)`

B

`5^(@)`

C

`15^(@)`

D

`2.5^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that ,
`r + r. = A`
Given that the ray of light emerges from the other face normally,
`:. R. = 0`
`rArr r = A - r. = 5 - 0 = 5^(@)`
Also `mu = (sin i)/(sin r)`
`rArr sin I = mu sin r`
`= 1.5 xx sin 5^(@) = 1.5 xx 0.0871`
`= 0.1307`
`rArr i = sin^(-1) (0.1307)`
`= 75^(@)`
The correct option is (a).
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Knowledge Check

  • A ray of light incident at an angle theta on a refracting face of a prism emerges from the other face normally. If the angle of prism is 5^(@) and the prism is made of a material of refractive index 1.5, the angle of incidence is

    A
    `7.5^(@)`
    B
    `5^(@)`
    C
    `15^(@)`
    D
    `2.5^(@)`

  • A ray of light is incident normally on one face of a prism as shown in figure. The refractive index of the material of the prism is (5)/(3) and the prism is immersed in water of refractive index (4)/(3) , then

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    The angle of emergence `theta_(2)` of the ray is `sin^(-2)((5)/(8))`
    B
    The angle of emergence `theta_(2)` of the ray is `sin^(-1)((5)/(4sqrt(3)))`
    C
    The angle of emerrgence `theta_(2)` of the ray is `sin^(-1)((7)/(3sqrt(4)))`
    D
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    B
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    C
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    D
    3

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