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Ray Optics and Optical Instruments — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments1 Mark
MCQ
Two statements are given$-$one labelled Assertion $(A)$ and the other labelled Reason $(R)$. Select the correct answer to these questions from the codes $(a), (b), (c)$ and $(d)$ as given below.
Assertion: The focal length of an equiconvex lens placed in air is equal to radius of curvature of either face. Lens is made up of material of refractive index of $1.5.$
Reason: For an equiconvex lens, radius of curvature of both the faces is same.
  • A
    Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
  • ✓
    Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
  • C
    $A$ is true but $R$ is false.
  • D
    $A$ is false and $R$ is also false.
✓

Answer

Correct option: B.
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
For an equiconvex lens, $R_1= R_2= R$
From $\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big)$
Using lens maker's formula for glass, $\mu = 1.5$
placed in air $\frac{1}{\text{f}}=(1.5-1)\frac{2}{\text{R}}\Rightarrow\text{f}=\text{R}.$

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