JEE Physics/ Lakshmikanta Satapathy/ Ray Optics part 1/ Question on Image formation by a plane mirror of finite thickness solved using the concept of real depth and apparent depth

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L K Satapathy Geometrical Optics 1
Reflection by Plane Mirror
O

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L K Satapathy Geometrical Optics 1
Question : A plane mirror is made of glass of thickness 3 cm and refractive index 1.5 ,
by silvering one of its faces. A point object is placed at a distance of 6 cm in front of
the unsilvered face. The distance of the image from the silvered face is
(a) 6 cm (b) 7 cm (c) 12 cm (d) 15 cm
A BOI1 I2I3
C
D
E
F
The ray OC from the object O ,
is incident on the unsilvered
face at C. It is then refracted
along CD and incident on the
silvered face at D. It is then
reflected along DE and
incident on the unsilvered face
at E where it is again refracted
and finally it moves along EF.
Answer :
The process :

3. Physics Helpline
L K Satapathy Geometrical Optics 1
(i) Refraction at C
A BOI1
C
DThe incident ray OC travelling from rarer to denser
medium , bends towards the normal and moves along
CD. On producing backwards , it meets the principal
axis and forms an image at I1 .
Given : Thickness of mirror , AB = 3 cm
Object distance OA = 6 cm
 Viewing from the glass side , the real depth = and the apparent depth =
Light is travelling from air ( = 1) to glass ( = 1.5)
Apparent depth = Real Depth
OA 1I A
glass 
1 1.5 6 9 . . . (1)glassI A OA cm     

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L K Satapathy Geometrical Optics 1
A BOI1 I2I3
C
D
E
F
(ii) Reflection at D :
 Object distance 1 1I B I A AB  9 3 12cm  
For reflection at a plane mirror : Object distance = Image distance
2 1 12 . . . (2)I B I B cm  
Object is at and the image is formed at1I 2I

5. Physics Helpline
L K Satapathy Geometrical Optics 1
A BOI1 I2I3
C
D
E
F
(iii) Refraction at E :
Real depth
Image is formed at2I 3I
Light is travelling from glass to air
Object is at
2 2 12 3 15I A I B AB cm      Apparent depth 3I A
glass
Real depth
Apparent depth

 
2
3
15
10
1.5glass
I A
I A cm

    3 3 10 3 7I B I A AB cm     
 Distance of the final image from the unsilvered face = 7 cm
Correct option = (b)

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L K Satapathy
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