Question

The maximum possible magnification for a simple microscope is 10

1. How do you increase the magnification further

2. Draw the ray diagram for compound microscope and find an expression for magnification

3. What is the advantage of forming image at infinity?

Answer 1

1. Use two convex lens instead of single lens.

2. 

The magnification produced by the compound microscope

m = \(\frac{size\,of\,the\,image}{size\,of\,the\,object}\) 

i.e, m = \(\frac{I_2M_2}{OB}\)

Multiplying and dividing by I₁M₁ we get,

m = \(\frac{I_2M_2}{I_1M_1}\times\frac{I_1M_1}{OB}\)

but we know, m_e = \(\frac{I_2M_2}{I_1M_1}\)and m_o = \(\frac{I_1M_1}{OB}\)

Where m₀ & m_e are the magnifying power of objective lens and eyepiece lens.

∴ m = m_e × m₀   .......(1)

Eyepiece acts as a simple microscope.

Therefore m_e = 1 + \(\frac{D}{f_e}\)  .....(2)

We know magnification of objective lens

m₀ = \(\frac{V_0}{u_0}\) .....(3)

Where v₀ and u₀ are the distance of the image and object from the objective lens.

Substituting (2) and (3) in (1), we get

m = \(\frac{-V_0}{u_0}\Big(1+\frac{D}{f_e}\Big)\)

for compound microscope, u₀ » f₀ (because the object of is placed very close to the principal focus of the objective) and v₀ ≈ L, length of microscope (because the first image is formed very close to the eye piece).

m = \(\frac{-L}{f_0}\Big(1+\frac{D}{f_e}\Big)\)

where L is the length of microscope, f₀ is the focal length of objective lens.

3. Strain for eye, will be minimum when image is at infinity.