The focal lengths of the lenses of an astrono | vedclass

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(D) For an astronomical telescope,the focal length of the objective lens is $f_o = 50\, cm$ and the focal length of the eyepiece is $f_e = 5\, cm$.The

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$\frac{325}{6}\, cm$

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(D) For an astronomical telescope,the focal length of the objective lens is $f_o = 50\, cm$ and the focal length of the eyepiece is $f_e = 5\, cm$.The length of the telescope tube $L$ when the final image is formed at the least distance of distinct vision $(D = 25\, cm)$ is given by the formula:$L = f_o + u_e$where $u_e$ is the object distance for the eyepiece.Using the lens formula for the eyepiece: $\frac{1}{v_e} - \frac{1}{u_e} = \frac{1}{f_e}$.Here,$v_e = -D = -25\, cm$,so $\frac{1}{-25} - \frac{1}{u_e} = \frac{1}{5}$.$\frac{1}{u_e} = -\frac{1}{25} - \frac{1}{5} = \frac{-1 - 5}{25} = -\frac{6}{25}$.Thus,$u_e = \frac{25}{6}\, cm$.The length of the telescope is $L = 50 + \frac{25}{6} = \frac{300 + 25}{6} = \frac{325}{6}\, cm$.

The focal lengths of the lenses of an astronomical telescope are $50\, cm$ and $5\, cm$. The length of the telescope when the image is formed at the least distance of distinct vision is

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