MHT CET · Physics · Ray Optics

A double convex lens made of glass has both radii of curvature of magnitude \(20 \mathrm{~cm}\). Incident light rays parallel to the axis of the lens will converge to a point at a distance ' \(L\) ' from the common pole P. The value of L is [Refractive index of glass \(=1.5\) ]

A \(10 \mathrm{~cm}\)
B \(40 \mathrm{~cm}\)
C \(\frac{20}{3} \mathrm{~cm}\)
D \(20 \mathrm{~cm}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(20 \mathrm{~cm}\)

Step-by-step Solution

Detailed explanation

Lens maker formula: \(\frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right)\)
If incidence ray has direction left to right \&
\(\left|R_1\right|=\left|R_2\right|=20 \mathrm{~cm}=\mathrm{R}, \mu=1.5\), then
\(\begin{aligned} & \frac{I}{f}=(\mu-1)\left(\frac{1}{R}-\frac{1}{(-R)}\right)=\frac{2(\mu-1)}{R} \\ & =\frac{2(1.5-1)}{20 \mathrm{~cm}} \\ & \Rightarrow f=20 \mathrm{~cm}\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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