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

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments1 Mark
Question
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.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false and R is also false.
Assertion: A double convex lens $(\mu = 1.5)$ has focal length 10cm. When the lens is immersed in water $\big(\mu=\frac{4}{3}\big)$ its focal length becomes 78.24cm.
Reason: $\frac{1}{\text{f}}=\frac{\mu_\text{g}-\mu_\text{m}}{\mu_\text{m}}\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big).$
✓

Answer

  1. Both A and R are true and R is the correct explanation of A.

Explanation:

$\frac{1}{\text{f}}=(^\text{w}\mu_\text{g}-1)\Big[\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big]$

$=\Big(\frac{\mu_\text{g}}{\mu_\text{w}}-{1}\Big)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big)$

$\frac{1}{\text{f}}=\Big(\frac{\mu_\text{g}-\mu_\text{w}}{\mu_\text{w}}\Big)\times\Big[\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big]$

$=\Big(\frac{1.5-1.33}{1.33}\Big)\times\Big[\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big]$

$\therefore\text{f}=78.24\text{cm}$

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