Chapter Test: Ray Optics and Optical Instruments - 1 JEE Physics Free MCQs

Option D is correct.

1/f = (μ_inside / μ_outside - 1) (1/R1 - 1/R2)

This is the lens-maker form for a thin lens when the lens substance (here the fluid filling the hollow lens) has refractive index μ_inside and the surrounding medium has refractive index μ_outside. The geometrical factor (1/R1 - 1/R2) for a double-concave shape is negative.

Therefore the sign of f (whether the lens is converging or diverging) follows the sign of (μ_inside / μ_outside - 1). To keep the concave lens diverging (negative focal length), we require μ_inside / μ_outside > 1, i.e., the filling must have a higher refractive index than the surrounding medium.

Given μ₂ > μ₁, choosing μ_inside = μ₂ and μ_outside = μ₁ (that is, filling with L₂ and immersing in L₁) satisfies this condition, so the lens remains diverging.

For reference: if the lens is filled with air and placed in air then μ_inside / μ_outside = 1 and f → ∞ (no lensing). If the filling has a smaller index than the surrounding medium (μ_inside < μ_outside), the concave shape would act as a converging lens.

Final: fill with L₂ and immerse in L₁ (Option D).

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In a convex lens,  (1/v)−(1/u)=(1/f)​
Or (1/v)​−(1/f)​=(1/u)​ where u is always negative and f is always positive.
(1/v)​=(1/f)​−(1/u)​
So, as u is increased 1/u will decrease and  (1/f)​−(1/u)​  will increase, so, 1/v​ increases or v decreases.
So, its graph will be a hyperbola

P=P1​+P2​=+2−1=+1 dioptre, lens behaves as convergent
F=1​/P=1/1​=1m=100cm

In air, all the colours of light travel with the same velocity with the same velocity, but in glass, velocities of different colours are different. Velocity of red colour is largest and velocity of violet colour is smallest. Therefore, after travelling through the glass slab, red colour will emerge first.

When the deviation is minimum, then the incidence angle and emergence angle are equal and this is possible only when the refracted ray inside the prism is parallel to the base of the prism. 
Minimum deviation is given by δ=2i−A, where A is prism angle.

Magnifying power of a compound- microscope is given by m=− (l​D​/f₀​f_e​)
where, l is length of tube
D is least distance of clear vision
f₀​ is focal length of objective
f_e​ is focal length of eyepiece
So, clearly, it can be seen that focal length of objective and eyepiece needs to be decreased so that magnifying power increases.