Optics Problem: Solving for Refraction on a Spherical Surface

[thunderhadron]

Hi friends Please help me in solving this issue too.

The problem is as follows :

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash3/526477_2890689763636_1631084369_n.jpg

As it seems that the rays are striking on the the spherical surface parallel to the principal axis so u → ∞.

Applying formal for the refraction by the spherical surface,

(μ₂ / v) - (μ₁ / u) = (μ₂ - μ₁)R

[(3/2) / v] - (1 / ∞) = (3/2 - 1) / R

After solving this v = R/3

So now the figure will be as this
https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-ash4/395622_2890690483654_116955071_n.jpg

Here the left upper side and right upper side right angle triangles are similar ones. So applying the property of the similar triangles,

perpendicular over base for the first triangle = perpendicular over base for the second triangle

so

[d' / (2R/3)] = [d / (r/3)]

After solving this d' = 2d

but friends the answer is given 2d / 3.

Please friends apply your sound information here also.

Thank you very much in advance.

 

[Saitama]

Check your value of v again.

 

[thunderhadron]

Thank you very much Pranav.

I got the answer.