a ray of light is incident on a surface of glass slab at angle 45 degree if lateral shift produced per thickness is 1/root3 meter then r is
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1
Correct option is
B
tan
−1
(1−
3
2
)
Lateral shift, Y=
cosr
tsin(i−r)
t
Y
=
cosr
sin(i−r)
=
cosr
sinicosr−cosisinr
[using identity, sin(A−B)=sinA⋅cosB−cosA⋅sinB]
=sini−cositanr
⇒
3
1
=sin45
o
−cos45
o
tanr=
2
1
(1−tanr)
⇒
3
2
=1−tanr
⇒tanr=1−
3
2
∴r=tan
−1
(1−
3
2
).
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