In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is (5)^k
Q. In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm . Total magnification obtained with this system for normal adjustment is \( (5)^k \). The value of \(k\) is ____ .

(A) 4

(B) 5

(C) 2

(D) 3.5

Correct Answer: 2

Explanation (Complete Step by Step Calculation)

For a compound microscope in normal adjustment, the total magnification is given by:

\[ M = \frac{L}{f_o} \times \frac{D}{f_e} \]

where \(L\) is the tube length, \(f_o\) is the focal length of objective lens, \(f_e\) is the focal length of eyepiece and \(D = 25 \, \text{cm}\).

Given values are:

\[ L = 10 \, \text{cm}, \quad f_o = 2 \, \text{cm}, \quad f_e = 5 \, \text{cm} \]

Substitute the values:

\[ M = \frac{10}{2} \times \frac{25}{5} \]
\[ M = 5 \times 5 \]
\[ M = 25 \]

Since:

\[ 25 = 5^2 \]

Comparing with \( (5)^k \), we get:

\[ k = 2 \]

Hence, the value of \(k\) is 2.

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