A glass cylindrical vessel with base concave mirror of focal length 20 cm is filled with two immiscible liquids of refractive index 1.5 and 1.4. Thickness of liquid level are 15cm and 14cm respectively.A fish is moving vertically upward along principle axis of mirror with a speed of 1 cm/s .A bird is moving along vertically downward direction with 2cm/s.A small hole is made at bottom surface of vessel. When distance of fish from pole of mirror is 10cm.the rate of liquid level falling is 1cm/s.(focal length of concave mirror is 20cm). Then at a given instant
A) velocity of image of fish formed after reflection from mirror is 1cm/s upward
B) velocity of image of fish formed after reflection from mirror is 1cm/s downward
C)velocity of fish as seen by itself is 5cm/s along downward direction
C)velocity of fish as seen by itself is 5cm/s along vertically downward direction
(this is a one or more correct type question)
Answers
Answer:
Given: The bottom of a container is 14.0 cm thick glass (μ=1.5) slab.The container contains two immiscible liquids A and B of depths 6.0 cm and 8.0 cm respectively. Refractive indices of A and B are 1.4 and 1.3 respectively.
To find the apparent position of a scratch on the outer surface of the bottom of the glass slab when viewed through the container
Solution:
The total apparent shift of the scratch on the outer surface is obtained by considering refraction at all the three media.
I.e.,
t
1
(1−
μ
1
1
)+t
2
(1−
μ
2
1
)+t
3
(1−
μ
3
1
)
where t
1
,t
2
,t
3
are the thickness of the glass, liquid A,liquid B respectively.
and μ
1
,μ
2
,μ
3
are the refractive index of glass, liquid A, liquid B respectively.
⟹=14(1−
1.5
1
)+6(1−
1.4
1
)+8(1−
1.3
1
)
⟹=14(0.33)+6(0.28)+8(0.23)
⟹=4.62+1.68+1.84
⟹=8.14
is the apparent position of a scratch on the outer surface of the bottom of the glass slab when viewed through the container
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