Assertion: A double convex lens ((μ=1.5)) has focal length (10 ~cm). When the lens is immersed in water ((μ=4 / 3)) its focal length becomes (77 ~cm). Reason : ((1)/(f)=(μ_g-μ_w)/(μ_w)((1)/(R_1)-(1)/(R_2)))

Correct answer: A. If both assertion and reason are true and reason is the correct explanation of assertion aligned & (1)/(f)=( ^a μ_g-1)[(1)/(R_1)-(1)/(R_2)] & =((μ_g)/(μ_w)-1)((1)/(R_1)-(1)/(R_2)) & (1)/(f)=((μ_g-μ_w)/(μ_w)) ·[(1)/(R_1)-(1)/(R_2)] & =((1.5-1.33)/(1.33)) ·[(1)/(20)+(1)/(20)] & (1)/(f)=(0.13 × 2)/(20) f=(20)/(0.26) & f=76.92 cm . & aligned

AIIMS 2008

Exam: AIIMS
Year: 2008
Subject: Physics
Chapter: Ray Optics

AIIMS 2008 · Physics · Ray Optics

Assertion: A double convex lens ((μ=1.5)) has focal length (10...

Assertion: A double convex lens ((\mu=1.5)) has focal length (10 \mathrm{~cm}). When the lens is immersed in water ((\mu=4 / 3)) its focal length becomes (77 \mathrm{~cm}). Reason : (\frac{1}{f}=\frac{\mu_g-\mu_w}{\mu_w}\left(\frac{1}{R_1}-\frac{1}{R_2}\right))

Options

AIf both assertion and reason are true and reason is the correct explanation of assertion
BIf both assertion and reason are true but reason is not the correct explanation of assertion
CIf assertion is true but reason is false
DIf both assertion and reason are false.

Correct answer

A. If both assertion and reason are true and reason is the correct explanation of assertion

Step-by-step solution

\begin{aligned} & \text{ } \frac{1}{f}=\left({ }^a \mu_g-1\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right] \\ & =\left(\frac{\mu_g}{\mu_w}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \\ & \frac{1}{f}=\left(\frac{\mu_g-\mu_w}{\mu_w}\right) \cdot\left[\frac{1}{R_1}-\frac{1}{R_2}\right] \\ & =\left(\frac{1.5-1.33}{1.33}\right) \cdot\left[\frac{1}{20}+\frac{1}{20}\right] \\ & \frac{1}{f}=\frac{0.13 \times 2}{20} \Rightarrow f=\frac{20}{0.26} \\ & \therefore f=76.92 \mathrm{ cm} \text{. } \\ & \end{aligned}

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