Question 85: Ray Optics

Question

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 $\_\_\_\_$ .

Accepted Answer

A compound microscope consists of two lenses objective lens (lens near the object) and the eyepiece (lens near the eye.). To achieve high magnification, objective lens must have a small focal length compared to eyepiece.
So,
1. Focal length of Objective $=f_0=2 \mathrm{~cm}$
2. Focal length of Eyepiece $=\mathrm{f}_{\mathrm{e}}=5 \mathrm{~cm}$
During normal adjustment in optical instruments the final image is formed at infinity. This allows the observer to view the image with a relaxed eye.
The total magnification ( M ) of a microscope is the product of the magnification of the objective ( $\mathrm{m}_{\mathrm{o}}$ ) and the magnification of the eyepiece ( $\mathrm{m}_{\mathrm{e}}$ ).
$$ \mathrm{M}=\mathrm{m}_{\mathrm{o}} 	imes \mathrm{m}_{\mathrm{e}} $$
The eyepiece acts like a simple magnifying glass. For an image formed at infinity, the angular magnification is the ratio of the distinct vision distance (D) to the focal length ( $\mathrm{f}_{\mathrm{e}}$ ).
$$ m_e=\frac{D}{f_e} $$
Where Least Distance of Distinct Vision $\mathrm{D}=25 \mathrm{~cm}$.
The objective forms a real, inverted image.
The tube length $(\mathrm{L})$ is defined as the distance between the second focal point of the objective and the first focal point of the eyepiece.
$$ m_o \approx \frac{L}{f_o} $$
So, the total magnification of the microscope is,
$$ \mathrm{M}=\left(\frac{\mathrm{L}}{\mathrm{f}_{\mathrm{o}}}ight) 	imes\left(\frac{\mathrm{D}}{\mathrm{f}_{\mathrm{e}}}ight) $$
Putting the values,
$$ M=\left(\frac{10 \mathrm{~cm}}{2 \mathrm{~cm}}ight) 	imes\left(\frac{25}{5}ight)=25=5^2 $$
$$\Rightarrow $$ $$ 5^2=5^k \Rightarrow k=2 $$
Therefore, the value of k is 2.
Hence, the correct option is (C).

Answer

4

Answer

5

Answer

2

Answer

3.5

Ray Optics

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 \_\_\_\_ .

Choose the correct answer: