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Define critical angle with reference to ...

Define critical angle with reference to total internal reflection.
Calculate the critical angle for glass-air surface, if a ray of light which is incident in air on the glass surface is deviated through 15°, when angle of incidence is 45°.

Text Solution

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The critical angle for a pair of media may be defined as the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90° and beyond which the light is totally internally reflected back in the denser medium itself. In present problem angle of incidence in air i = 45°.
As the ray deviates through 15° on entering into glass and glass is optically denser, hence,
`r = 45^(@) 15^(@) = 30^(@)`
`therefore` Refractive index of glass `n_(ga) = (sin i)/(sin r) =(sin 45^(@))/(sin 30^(@)) = (1//sqrt(2))/(1//2) = sqrt(2)`
`therefore` Critical angle for glass-air interface is given by `sin i_( c) = 1/(n_(ga)) = 1/sqrt(2) rArr i_( c) = sin^(-1) (1/sqrt(2)) = 45^(@)`
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Calculate the critical angle for glass air surface if a ray of light which is incident in air on the glass surface is deviated through 15^@ , when the angle of incidence is 45^@ .

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Knowledge Check

  • Glass has refractive index mu with respect to air and the critical angle for a ray of light going from glass to air is theta . If a ray of light is incident from air on the glass with angle of incidence theta , the corresponding angle of refraction is

    A
    `sin^(-1)((1)/(sqrt(mu)))`
    B
    `90^(@)`
    C
    `sin^(-1)((1)/(mu^(2)))`
    D
    `sin^(-1)((1)/(mu))`

  • Total internal reflection of a ray of light is possible when the ( i_(c) = critical angle, i= angle of incidence)

    A
    Ray goes from denser medium to rarer medium and `i lt i_(c)`
    B
    Ray goes from denser medium to rarer medium and `i gt i_(c)`
    C
    Ray goes from rarer medium to denser medium and `i gt i_(c)`
    D
    Ray goes from rarer medium to denser medium and `i lt i_(c)`

  • The Brwster angle of the glass-air interface is 54.74^(@) . If a ray of light going from air to glass strikes at an angle of incidence 45^@ , then the angle of refraction is

    A
    `60^(@)`
    B
    `30^(@)`
    C
    `25^(@)`
    D
    `54.74^(@)`

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