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(B) Given: Focal length of objective lens $f_o = 100 \, cm$. Total length of the telescope $L = 105 \, cm$. Least distance of distinct vision $v_e = -

Vedclass · Accepted Answer

$6.25$

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(B) Given: Focal length of objective lens $f_o = 100 \, cm$. Total length of the telescope $L = 105 \, cm$. Least distance of distinct vision $v_e = -25 \, cm$. We know that the length of the telescope is $L = f_o + |u_e|$,where $|u_e|$ is the object distance for the eyepiece. $|u_e| = L - f_o = 105 - 100 = 5 \, cm$. Thus,$u_e = -5 \, cm$. Using the lens formula for the eyepiece: $\frac{1}{f_e} = \frac{1}{v_e} - \frac{1}{u_e}$. Substituting the values: $\frac{1}{f_e} = \frac{1}{-25} - \frac{1}{-5} = -0.04 + 0.2 = 0.16$. Therefore,$f_e = \frac{1}{0.16} = 6.25 \, cm$.

The objective lens of a telescope has a focal length of $100 \, cm$. When the final image is formed at the least distance of distinct vision,the distance between the lenses is $105 \, cm$. Calculate the focal length of the eyepiece in $cm$.

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