Question

A glass rod has ends as shown in fig. The refractive
index of glass is u. The object O is at a distance 2
R from the surface of larger radius of curvature.
The distance between apexes of ends is 3R. Find
the distance of image formed of the point object
from right hand vertex.​

Answer 1

Answer:

• v =2μR /( 2μ -3)

Explanation:

GIVEN:

•   The refractive index of glass is u.

•   The object O is at a distance 2R from the surface of larger radius of  curvature.
•   The distance between apexes of ends is 3R.

TO FIND,

•   the distance of image formed of the point object from right hand vertex.​

SOLUTION:

    We know that,

    μ₂/v - μ₁/u =  (μ₂- μ₁)/R   --------------(1)

   Here,

•  μ₁ = μ(air) =1
• μ₂ = μ(glass) = μ
• u = object distance
• v= image distance

• u = -2R ( negative sign because when the light rays enters the glass at an origin it moves in positive x axis inside the glass but the light rays outside the glass isin negative x axis)
• subtituting these values in equation(1)
• μ/v - 1/(-2R) =  (μ- 1)/R
• μ/v +1/(2R) =  (μ- 1)/R
• μ/v =  (μ- 1)/R -1/(2R)
• multiplying right side with 2,hence we get equal denominator
• μ/v =  2(μ- 1)/2R -1/(2R)
• μ/v = ( 2μ -2-1)/2R
• μ/v = ( 2μ -3)/2R
• v =2μR /( 2μ -3) -------------(2) (IMAGE DISTANCE

Now,the total distance of the glass is 3R, here v is the image distance at origin of the glass to thr centre where u is the object distancew from the centre if the glass to the end.

Hence , the distance of image formed of the point object from right hand vertex

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