Question

the focal length of the transparent sphere of radius R and refractive index n is equals to​

Answer 1

Answer:

A transparent sphere of radius R and refractive index μ is kept in the air.  

To find the distance from the surface of the sphere where a point should be placed so as to form a real image at the same distance from the other side of the sphere

Solution:

Using the equation,  

v

μ  

2

​  

 

​  

−  

u

μ  

1

​  

 

​  

=  

R

μ  

2

​  

−μ  

1

​  

 

​  

 

For the refraction at the first surface of the sphere,  

(air to glass)

∞

μ

​  

−  

−x

1

​  

=  

R

μ−1

​  

, Here x is the distance of point object from the sphere, as shown in above fig.

⟹  

x

1

​  

=  

R

μ−1

​  

 

⟹x=  

μ−1

R

​  

 

Hence the object should be placed this distance from the surface of the sphere in order to get real image

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Explanation: