364949
With respect to air critical angle in a medium for light of red colour \(\left[ {{\lambda _1}} \right]\) is \(\theta \) Other facts remaining same, critical angle for light of yellow colour \(\left[ {{\lambda _2}} \right]\) will be
364950
A ray of light enters from a rarer to a denser medium. The angle of incidence is \(i\). Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is
1 \({\sin ^{ - 1}}\left( {\cot i} \right)\)
2 \({\cos ^{ - 1}}\left( {\tan i} \right)\)
3 \({\sin ^{ - 1}}\left( {\tan i} \right)\)
4 \({\tan ^{ - 1}}\left( {\sin i} \right)\)
Explanation:
From figure (a), \(90^\circ - i + 90^\circ - r = 90^\circ \) \(\therefore \,\,\,\,\,i + r = {90^o}\) \( \Rightarrow \mu = \frac{{\sin i}}{{\sin r}} = \frac{{\sin i}}{{\sin \left( {{{90}^o} - i} \right)}} = \tan i\) From figure (b), \(\frac{{\sin {{90}^o}}}{{\sin C}} = \mu \Rightarrow \sin C = \frac{1}{\mu } = \cot i\) \(\therefore \) Critical angle C = \({\sin ^{ - 1}}\left( {\cot i} \right)\)
KCET - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364951
For total internal reflection to take place, the angle of incidence \(i\) and the refractive index \(\mu \) of the medium must satisfy the inequality
1 \(\sin i < \mu \)
2 \(\frac{1}{{\sin i}} < \mu \)
3 \(\sin i < \mu \sin i < \mu \)
4 \(\frac{1}{{\sin i}} > \mu \)
Explanation:
For total internal reflection \(i > C\) \( \Rightarrow \sin i > \sin C \Rightarrow \sin i > \frac{1}{\mu } \Rightarrow \frac{1}{{\sin i}} < \mu .\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364952
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains
1 Yellow, orange, red
2 Violet, indigo, blue
3 All colours
4 All colours except green
Explanation:
As \({\lambda _R} > {\lambda _V} \Rightarrow {\mu _V} > {\mu _R}\;\;\;\;\;\;(1)\) For TIR \(\sin \theta = \frac{1}{\mu } \Rightarrow \theta {\mkern 1mu} \alpha \frac{1}{\mu }\;\;\;\;\;\;(2)\) From (1) & (2) \({\theta _R} > {\theta _V}\) Where \({\theta _r}\& {\theta _R}\) are critical angle for violet and red. If green undergoes TIR then Y, O & R pass through air.
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364949
With respect to air critical angle in a medium for light of red colour \(\left[ {{\lambda _1}} \right]\) is \(\theta \) Other facts remaining same, critical angle for light of yellow colour \(\left[ {{\lambda _2}} \right]\) will be
364950
A ray of light enters from a rarer to a denser medium. The angle of incidence is \(i\). Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is
1 \({\sin ^{ - 1}}\left( {\cot i} \right)\)
2 \({\cos ^{ - 1}}\left( {\tan i} \right)\)
3 \({\sin ^{ - 1}}\left( {\tan i} \right)\)
4 \({\tan ^{ - 1}}\left( {\sin i} \right)\)
Explanation:
From figure (a), \(90^\circ - i + 90^\circ - r = 90^\circ \) \(\therefore \,\,\,\,\,i + r = {90^o}\) \( \Rightarrow \mu = \frac{{\sin i}}{{\sin r}} = \frac{{\sin i}}{{\sin \left( {{{90}^o} - i} \right)}} = \tan i\) From figure (b), \(\frac{{\sin {{90}^o}}}{{\sin C}} = \mu \Rightarrow \sin C = \frac{1}{\mu } = \cot i\) \(\therefore \) Critical angle C = \({\sin ^{ - 1}}\left( {\cot i} \right)\)
KCET - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364951
For total internal reflection to take place, the angle of incidence \(i\) and the refractive index \(\mu \) of the medium must satisfy the inequality
1 \(\sin i < \mu \)
2 \(\frac{1}{{\sin i}} < \mu \)
3 \(\sin i < \mu \sin i < \mu \)
4 \(\frac{1}{{\sin i}} > \mu \)
Explanation:
For total internal reflection \(i > C\) \( \Rightarrow \sin i > \sin C \Rightarrow \sin i > \frac{1}{\mu } \Rightarrow \frac{1}{{\sin i}} < \mu .\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364952
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains
1 Yellow, orange, red
2 Violet, indigo, blue
3 All colours
4 All colours except green
Explanation:
As \({\lambda _R} > {\lambda _V} \Rightarrow {\mu _V} > {\mu _R}\;\;\;\;\;\;(1)\) For TIR \(\sin \theta = \frac{1}{\mu } \Rightarrow \theta {\mkern 1mu} \alpha \frac{1}{\mu }\;\;\;\;\;\;(2)\) From (1) & (2) \({\theta _R} > {\theta _V}\) Where \({\theta _r}\& {\theta _R}\) are critical angle for violet and red. If green undergoes TIR then Y, O & R pass through air.
364949
With respect to air critical angle in a medium for light of red colour \(\left[ {{\lambda _1}} \right]\) is \(\theta \) Other facts remaining same, critical angle for light of yellow colour \(\left[ {{\lambda _2}} \right]\) will be
364950
A ray of light enters from a rarer to a denser medium. The angle of incidence is \(i\). Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is
1 \({\sin ^{ - 1}}\left( {\cot i} \right)\)
2 \({\cos ^{ - 1}}\left( {\tan i} \right)\)
3 \({\sin ^{ - 1}}\left( {\tan i} \right)\)
4 \({\tan ^{ - 1}}\left( {\sin i} \right)\)
Explanation:
From figure (a), \(90^\circ - i + 90^\circ - r = 90^\circ \) \(\therefore \,\,\,\,\,i + r = {90^o}\) \( \Rightarrow \mu = \frac{{\sin i}}{{\sin r}} = \frac{{\sin i}}{{\sin \left( {{{90}^o} - i} \right)}} = \tan i\) From figure (b), \(\frac{{\sin {{90}^o}}}{{\sin C}} = \mu \Rightarrow \sin C = \frac{1}{\mu } = \cot i\) \(\therefore \) Critical angle C = \({\sin ^{ - 1}}\left( {\cot i} \right)\)
KCET - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364951
For total internal reflection to take place, the angle of incidence \(i\) and the refractive index \(\mu \) of the medium must satisfy the inequality
1 \(\sin i < \mu \)
2 \(\frac{1}{{\sin i}} < \mu \)
3 \(\sin i < \mu \sin i < \mu \)
4 \(\frac{1}{{\sin i}} > \mu \)
Explanation:
For total internal reflection \(i > C\) \( \Rightarrow \sin i > \sin C \Rightarrow \sin i > \frac{1}{\mu } \Rightarrow \frac{1}{{\sin i}} < \mu .\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364952
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains
1 Yellow, orange, red
2 Violet, indigo, blue
3 All colours
4 All colours except green
Explanation:
As \({\lambda _R} > {\lambda _V} \Rightarrow {\mu _V} > {\mu _R}\;\;\;\;\;\;(1)\) For TIR \(\sin \theta = \frac{1}{\mu } \Rightarrow \theta {\mkern 1mu} \alpha \frac{1}{\mu }\;\;\;\;\;\;(2)\) From (1) & (2) \({\theta _R} > {\theta _V}\) Where \({\theta _r}\& {\theta _R}\) are critical angle for violet and red. If green undergoes TIR then Y, O & R pass through air.
364949
With respect to air critical angle in a medium for light of red colour \(\left[ {{\lambda _1}} \right]\) is \(\theta \) Other facts remaining same, critical angle for light of yellow colour \(\left[ {{\lambda _2}} \right]\) will be
364950
A ray of light enters from a rarer to a denser medium. The angle of incidence is \(i\). Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is
1 \({\sin ^{ - 1}}\left( {\cot i} \right)\)
2 \({\cos ^{ - 1}}\left( {\tan i} \right)\)
3 \({\sin ^{ - 1}}\left( {\tan i} \right)\)
4 \({\tan ^{ - 1}}\left( {\sin i} \right)\)
Explanation:
From figure (a), \(90^\circ - i + 90^\circ - r = 90^\circ \) \(\therefore \,\,\,\,\,i + r = {90^o}\) \( \Rightarrow \mu = \frac{{\sin i}}{{\sin r}} = \frac{{\sin i}}{{\sin \left( {{{90}^o} - i} \right)}} = \tan i\) From figure (b), \(\frac{{\sin {{90}^o}}}{{\sin C}} = \mu \Rightarrow \sin C = \frac{1}{\mu } = \cot i\) \(\therefore \) Critical angle C = \({\sin ^{ - 1}}\left( {\cot i} \right)\)
KCET - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364951
For total internal reflection to take place, the angle of incidence \(i\) and the refractive index \(\mu \) of the medium must satisfy the inequality
1 \(\sin i < \mu \)
2 \(\frac{1}{{\sin i}} < \mu \)
3 \(\sin i < \mu \sin i < \mu \)
4 \(\frac{1}{{\sin i}} > \mu \)
Explanation:
For total internal reflection \(i > C\) \( \Rightarrow \sin i > \sin C \Rightarrow \sin i > \frac{1}{\mu } \Rightarrow \frac{1}{{\sin i}} < \mu .\)
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364952
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains
1 Yellow, orange, red
2 Violet, indigo, blue
3 All colours
4 All colours except green
Explanation:
As \({\lambda _R} > {\lambda _V} \Rightarrow {\mu _V} > {\mu _R}\;\;\;\;\;\;(1)\) For TIR \(\sin \theta = \frac{1}{\mu } \Rightarrow \theta {\mkern 1mu} \alpha \frac{1}{\mu }\;\;\;\;\;\;(2)\) From (1) & (2) \({\theta _R} > {\theta _V}\) Where \({\theta _r}\& {\theta _R}\) are critical angle for violet and red. If green undergoes TIR then Y, O & R pass through air.
