(D) For a simple microscope,the magnification is given by $m = 1 + \frac{D}{f_0}$.Given $m = 6$ and $D = 25 \, cm$,we have $6 = 1 + \frac{25}{f_0}$,wh

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(D) For a simple microscope,the magnification is given by $m = 1 + \frac{D}{f_0}$.Given $m = 6$ and $D = 25 \, cm$,we have $6 = 1 + \frac{25}{f_0}$,which implies $5 = \frac{25}{f_0}$,so $f_0 = 5 \, cm$.For a compound microscope,the total magnification $M$ for an image at infinity is given by $M = \frac{L \cdot D}{f_0 \cdot f_e}$,where $L$ is the tube length.Given $M = 2 \times 6 = 12$,$L = 0.6 \, m = 60 \, cm$,$D = 25 \, cm$,and $f_0 = 5 \, cm$,we substitute these values into the formula:$12 = \frac{60 \times 25}{5 \times f_e}$.$12 = \frac{1500}{5 \times f_e} = \frac{300}{f_e}$.$f_e = \frac{300}{12} = 25 \, cm$.

Class 12 Physics Ray Optics and Optical Instruments Microscope

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An object viewed from a near point distance of $25 \, cm$,using a microscopic lens with magnification $6$,gives an unresolved image. $A$ resolved image is observed at infinite distance with a total magnification double the earlier,using an eyepiece along with the given lens and a tube of length $0.6 \, m$. The focal length of the eyepiece is equal to $.... \, cm$.

JEE MAIN 2021 All JEE MAIN

A
$2.5$
B
$12$
C
$60$
D
$25$

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Ray Optics and Optical Instruments

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Microscope

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$A$ compound microscope is used to enlarge an object kept at a distance $0.03\,m$ from its objective,which consists of several convex lenses in contact and has a focal length of $0.02\,m$. If a lens of focal length $0.1\,m$ is removed from the objective,then by what distance must the eyepiece of the microscope be moved to refocus the image? (in $cm$)

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In a compound microscope,the focal lengths of two lenses are $1.5 \text{ cm}$ and $6.25 \text{ cm}$. An object is placed at $2 \text{ cm}$ from the objective and the final image is formed at $25 \text{ cm}$ from the eye lens. The distance between the two lenses is .............. (in $\text{cm}$).

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$A$ compound microscope has a magnifying power of $30$. The focal length of its eyepiece is $5 \, cm$. Assuming the final image is formed at the least distance of distinct vision,the magnification produced by the objective is:

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To improve the resolving power of a compound microscope, we should:

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In a compound microscope,the focal lengths of the objective and eye lens are $2.5 \, cm$ and $5 \, cm$ respectively. An object is placed at $3.75 \, cm$ in front of the objective. If the final image is formed at the least distance of distinct vision,then the distance between the two lenses (length of the microscope tube) is.......$cm$.

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In a compound microscope,the focal lengths of two lenses are $1.5 \text{ cm}$ and $6.25 \text{ cm}$. An object is placed at $2 \text{ cm}$ from the objective and the final image is formed at $25 \text{ cm}$ from the eye lens. The distance between the two lenses is .............. (in $\text{cm}$).

$A$ compound microscope has a magnifying power of $30$. The focal length of its eyepiece is $5 \, cm$. Assuming the final image is formed at the least distance of distinct vision,the magnification produced by the objective is:

To improve the resolving power of a compound microscope, we should:

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