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JEE Main Physics Class 12 Ray Optics and Optical Instruments Part 1 Questions
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© examsnet.com
Question : 67
Total: 99
A light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to :
[Online April 23, 2013]
(
√
2
+
1
)
2
√
5
2
3
2
√
3
2
Validate
Solution:
At point A by Snell's law
µ
=
sin
45
°
sin
r
⇒
sin
r
=
1
µ
√
2
.......(i)
At point B, for total internal reflection,
sin
i
1
=
1
µ
From figure,
i
1
=
90
°
−
r
∴
(
sin
90
°
−
r
)
=
1
µ
⇒
cos
r
=
1
µ
.......(ii)
Now
cos
r
=
√
1
−
sin
2
r
=
√
1
−
1
2
µ
2
=
√
2
µ
2
−
1
2
µ
2
.......(iii)
From eqs (ii) and (iii)
1
µ
=
√
2
µ
2
−
1
2
µ
2
Squaring both sides and then solving, we get
µ
=
√
3
2
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