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Question:

The diameter of the objective lens of a microscope makes an angle β at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index 'n'. Then the resolving power of the microscope:

Increases with decreasing value of n

Increases with decreasing value of β

Increases with increasing value of nsin2β

Increases with increasing value of 1/nsin2β

Solution:

Resolving Power of the Microscope is given by
1/d = (2nsinθ)/λ
where n is refractive index, θ is the angle of the cone and d is the distance between the object.
Here, The diameter of the objective lens of microscope makes an angle β at the focus of the microscope.
Hence, β = θ/2
Hence, resolving power is proportional to 2nsin2β/λ