Refraction at plane surface
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PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364966 A rectangular glass slab \(ABCD\) of refractive index \({\mu _1}\) is immersed in water of refractive index \({\mu _2}\left( {{\mu _1} > {\mu _2}} \right).\) A ray of light is incident at the surface \(AD{\rm{ }}\) of the slab as shown. The maximum value of the angle of incidence \({\alpha _{\max }},\) such that the ray comes out only from the other surface \(BC\) is given by
supporting img

1 \({\sin ^{ - 1}}\left( {\frac{{{\mu _2}}}{{{\mu _1}}}} \right)\)
2 \({\sin ^{ - 1}}\left[ {\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\cos \left( {{{\sin }^{ - 1}}\frac{{{\mu _2}}}{{{\mu _1}}}} \right)} \right]\)
3 \({\sin ^{ - 1}}\left[ {{\mu _1}.\cos \left( {{{\sin }^{ - 1}}\frac{1}{{{\mu _2}}}} \right)} \right]\)
4 \({\sin ^{ - 1}}\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364967 Assertion :
Air is rarer than glass.
Reason :
The light travelling from air to glass can not suffer total internal reflection.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364968 A fish is a little away below the surface of a lake. If the critical angle is 49° then the fish could see things above the water surface within an angular range of \(\theta ^\circ \) where
supporting img

1 \({\rm{\theta = 9}}{{\rm{0}}^0}\)
2 \({\rm{\theta = 4}}{{\rm{9}}^0}\)
3 \({\rm{\theta = 9}}{{\rm{8}}^0}\)
4 \({\rm{\theta = 24}}{\frac{1}{2}^0}\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364969 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

1 \(90^\circ \)
2 \({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt \mu }}} \right)\)
3 \({\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)\)
4 \({\sin ^{ - 1}}\left( {\frac{1}{{{\mu ^2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364970 A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is \(4 / 3\) and the fish is\(12\;cm\) below the surface of water, the radius of the circle in centimeter is

1 \(\frac{{12 \times 3}}{{\sqrt 5 }}\)
2 \(12 \times 3 \times \sqrt 5 \)
3 \(\frac{{12 \times 3}}{{\sqrt 7 }}\)
4 \(12 \times 3 \times \sqrt 7 \)
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PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364966 A rectangular glass slab \(ABCD\) of refractive index \({\mu _1}\) is immersed in water of refractive index \({\mu _2}\left( {{\mu _1} > {\mu _2}} \right).\) A ray of light is incident at the surface \(AD{\rm{ }}\) of the slab as shown. The maximum value of the angle of incidence \({\alpha _{\max }},\) such that the ray comes out only from the other surface \(BC\) is given by
supporting img

1 \({\sin ^{ - 1}}\left( {\frac{{{\mu _2}}}{{{\mu _1}}}} \right)\)
2 \({\sin ^{ - 1}}\left[ {\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\cos \left( {{{\sin }^{ - 1}}\frac{{{\mu _2}}}{{{\mu _1}}}} \right)} \right]\)
3 \({\sin ^{ - 1}}\left[ {{\mu _1}.\cos \left( {{{\sin }^{ - 1}}\frac{1}{{{\mu _2}}}} \right)} \right]\)
4 \({\sin ^{ - 1}}\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364967 Assertion :
Air is rarer than glass.
Reason :
The light travelling from air to glass can not suffer total internal reflection.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364968 A fish is a little away below the surface of a lake. If the critical angle is 49° then the fish could see things above the water surface within an angular range of \(\theta ^\circ \) where
supporting img

1 \({\rm{\theta = 9}}{{\rm{0}}^0}\)
2 \({\rm{\theta = 4}}{{\rm{9}}^0}\)
3 \({\rm{\theta = 9}}{{\rm{8}}^0}\)
4 \({\rm{\theta = 24}}{\frac{1}{2}^0}\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364969 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

1 \(90^\circ \)
2 \({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt \mu }}} \right)\)
3 \({\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)\)
4 \({\sin ^{ - 1}}\left( {\frac{1}{{{\mu ^2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364970 A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is \(4 / 3\) and the fish is\(12\;cm\) below the surface of water, the radius of the circle in centimeter is

1 \(\frac{{12 \times 3}}{{\sqrt 5 }}\)
2 \(12 \times 3 \times \sqrt 5 \)
3 \(\frac{{12 \times 3}}{{\sqrt 7 }}\)
4 \(12 \times 3 \times \sqrt 7 \)
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PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364966 A rectangular glass slab \(ABCD\) of refractive index \({\mu _1}\) is immersed in water of refractive index \({\mu _2}\left( {{\mu _1} > {\mu _2}} \right).\) A ray of light is incident at the surface \(AD{\rm{ }}\) of the slab as shown. The maximum value of the angle of incidence \({\alpha _{\max }},\) such that the ray comes out only from the other surface \(BC\) is given by
supporting img

1 \({\sin ^{ - 1}}\left( {\frac{{{\mu _2}}}{{{\mu _1}}}} \right)\)
2 \({\sin ^{ - 1}}\left[ {\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\cos \left( {{{\sin }^{ - 1}}\frac{{{\mu _2}}}{{{\mu _1}}}} \right)} \right]\)
3 \({\sin ^{ - 1}}\left[ {{\mu _1}.\cos \left( {{{\sin }^{ - 1}}\frac{1}{{{\mu _2}}}} \right)} \right]\)
4 \({\sin ^{ - 1}}\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364967 Assertion :
Air is rarer than glass.
Reason :
The light travelling from air to glass can not suffer total internal reflection.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364968 A fish is a little away below the surface of a lake. If the critical angle is 49° then the fish could see things above the water surface within an angular range of \(\theta ^\circ \) where
supporting img

1 \({\rm{\theta = 9}}{{\rm{0}}^0}\)
2 \({\rm{\theta = 4}}{{\rm{9}}^0}\)
3 \({\rm{\theta = 9}}{{\rm{8}}^0}\)
4 \({\rm{\theta = 24}}{\frac{1}{2}^0}\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364969 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

1 \(90^\circ \)
2 \({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt \mu }}} \right)\)
3 \({\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)\)
4 \({\sin ^{ - 1}}\left( {\frac{1}{{{\mu ^2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364970 A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is \(4 / 3\) and the fish is\(12\;cm\) below the surface of water, the radius of the circle in centimeter is

1 \(\frac{{12 \times 3}}{{\sqrt 5 }}\)
2 \(12 \times 3 \times \sqrt 5 \)
3 \(\frac{{12 \times 3}}{{\sqrt 7 }}\)
4 \(12 \times 3 \times \sqrt 7 \)
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PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364966 A rectangular glass slab \(ABCD\) of refractive index \({\mu _1}\) is immersed in water of refractive index \({\mu _2}\left( {{\mu _1} > {\mu _2}} \right).\) A ray of light is incident at the surface \(AD{\rm{ }}\) of the slab as shown. The maximum value of the angle of incidence \({\alpha _{\max }},\) such that the ray comes out only from the other surface \(BC\) is given by
supporting img

1 \({\sin ^{ - 1}}\left( {\frac{{{\mu _2}}}{{{\mu _1}}}} \right)\)
2 \({\sin ^{ - 1}}\left[ {\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\cos \left( {{{\sin }^{ - 1}}\frac{{{\mu _2}}}{{{\mu _1}}}} \right)} \right]\)
3 \({\sin ^{ - 1}}\left[ {{\mu _1}.\cos \left( {{{\sin }^{ - 1}}\frac{1}{{{\mu _2}}}} \right)} \right]\)
4 \({\sin ^{ - 1}}\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364967 Assertion :
Air is rarer than glass.
Reason :
The light travelling from air to glass can not suffer total internal reflection.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364968 A fish is a little away below the surface of a lake. If the critical angle is 49° then the fish could see things above the water surface within an angular range of \(\theta ^\circ \) where
supporting img

1 \({\rm{\theta = 9}}{{\rm{0}}^0}\)
2 \({\rm{\theta = 4}}{{\rm{9}}^0}\)
3 \({\rm{\theta = 9}}{{\rm{8}}^0}\)
4 \({\rm{\theta = 24}}{\frac{1}{2}^0}\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364969 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

1 \(90^\circ \)
2 \({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt \mu }}} \right)\)
3 \({\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)\)
4 \({\sin ^{ - 1}}\left( {\frac{1}{{{\mu ^2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364970 A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is \(4 / 3\) and the fish is\(12\;cm\) below the surface of water, the radius of the circle in centimeter is

1 \(\frac{{12 \times 3}}{{\sqrt 5 }}\)
2 \(12 \times 3 \times \sqrt 5 \)
3 \(\frac{{12 \times 3}}{{\sqrt 7 }}\)
4 \(12 \times 3 \times \sqrt 7 \)
Join With Us for More Updates
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364966 A rectangular glass slab \(ABCD\) of refractive index \({\mu _1}\) is immersed in water of refractive index \({\mu _2}\left( {{\mu _1} > {\mu _2}} \right).\) A ray of light is incident at the surface \(AD{\rm{ }}\) of the slab as shown. The maximum value of the angle of incidence \({\alpha _{\max }},\) such that the ray comes out only from the other surface \(BC\) is given by
supporting img

1 \({\sin ^{ - 1}}\left( {\frac{{{\mu _2}}}{{{\mu _1}}}} \right)\)
2 \({\sin ^{ - 1}}\left[ {\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\cos \left( {{{\sin }^{ - 1}}\frac{{{\mu _2}}}{{{\mu _1}}}} \right)} \right]\)
3 \({\sin ^{ - 1}}\left[ {{\mu _1}.\cos \left( {{{\sin }^{ - 1}}\frac{1}{{{\mu _2}}}} \right)} \right]\)
4 \({\sin ^{ - 1}}\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364967 Assertion :
Air is rarer than glass.
Reason :
The light travelling from air to glass can not suffer total internal reflection.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364968 A fish is a little away below the surface of a lake. If the critical angle is 49° then the fish could see things above the water surface within an angular range of \(\theta ^\circ \) where
supporting img

1 \({\rm{\theta = 9}}{{\rm{0}}^0}\)
2 \({\rm{\theta = 4}}{{\rm{9}}^0}\)
3 \({\rm{\theta = 9}}{{\rm{8}}^0}\)
4 \({\rm{\theta = 24}}{\frac{1}{2}^0}\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364969 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

1 \(90^\circ \)
2 \({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt \mu }}} \right)\)
3 \({\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)\)
4 \({\sin ^{ - 1}}\left( {\frac{1}{{{\mu ^2}}}} \right)\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS

364970 A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is \(4 / 3\) and the fish is\(12\;cm\) below the surface of water, the radius of the circle in centimeter is

1 \(\frac{{12 \times 3}}{{\sqrt 5 }}\)
2 \(12 \times 3 \times \sqrt 5 \)
3 \(\frac{{12 \times 3}}{{\sqrt 7 }}\)
4 \(12 \times 3 \times \sqrt 7 \)