Question

If the focal length of the objective lens is increased then the magnifying power of
A) Microscope will increase but that of telescopes decreases.
B) Microscope and telescope both will increase.
C) Microscope and telescope both will decrease.
D) Microscope will decrease but that of the telescope will increase

Answer 1

Hint: We have two equations for the magnifying power of a microscope and telescope. The magnifying power is related to the focal length of the objective lens. By analyzing their relationship, we can solve the question.

Formula used:
\[m=\dfrac{LD}{{{f}_{o}}\times {{f}_{e}}}\]
\[m=\dfrac{{{f}_{o}}}{{{f}_{e}}}\]

Complete step-by-step solution:
For a microscope, magnifying power is given by,
\[m=\dfrac{LD}{{{f}_{o}}\times {{f}_{e}}}\]
\[L\] is the tube length
\[D\] is the least distance of distinct vision.
\[{{f}_{o}}\] is the focal length of the objective lens
\[{{f}_{e}}\] is the focal length of the eye lens
From the above equation, we can see that \[m\] is inversely proportional to \[{{f}_{o}}\]. Hence if we increase the focal length of the objective lens, the magnifying power of the microscope will decrease. For a telescope, magnifying power is given by,
\[m=\dfrac{{{f}_{o}}}{{{f}_{e}}}\]
Where,
\[{{f}_{o}}\] is the focal length of the objective lens
\[{{f}_{e}}\] is the focal length of the eye lens
From the equation, we can see that, \[m\] is directly proportional to \[{{f}_{o}}\]
Hence, if we increase the focal length of the objective lens, the magnifying power of the telescope will increase.
Therefore, the answer is option D.

Note: For a telescope, magnifying power and focal length of eye lens are inversely related. Hence increasing the focal length of the eye lens will decrease the magnifying power. But in the case of a microscope, magnifying power is inversely related to the focal lens of the eye lens. The magnification produced by a simple microscope is small. It can only be increased by decreasing the focal length of the lens. Due to the practical limit in increasing the focal length, we use a compound microscope for large magnification in which magnification is obtained in two stages by using two convex lenses.