Question

2 38 An equiconvex lens has r = 40 cm and is
10 cm thick in the middle. If the
refractive index of the lens is 1.2, then
determine the position of the image from
the lens.

Answer 1

Given:

• Refractive index of lens $\mu = 1.2$

• Radius of lens $r = 40cm$

• Thickness of lens $d = 10cm$

To Find:

• Find the position of the image far away from the lens.

Solution:

We know that,

The focal length of a thick lens is given by

The Lens' Maker Formula-

      $\frac{1}{f} = (\mu - 1)(\frac{1}{R_1} - \frac{1}{R_2} + \frac{(\mu - 1)d}{\mu R_1 R_2} )$

Putting all the values

       $\frac{1}{f} = (1.2 - 1)(\frac{1}{40} - \frac{1}{-40} + \frac{(1.2 - 1)10}{1.2 \times 40 \times 40} )$

        $\frac{1}{f} = ( .2) (\frac{1}{40} + \frac{1}{40} + \frac{1}{ 960} )$

       $\frac{1}{f} = 0.2 (0.025 + 0.025 + 0.0010) \\\frac{1}{f} = 0.0102$

     $f = 98.03 cm$         

Hence, the image of object far from lens is formed at its focus, that is, at a distance $98.03cm$

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