SATHEE: Optics 3 Question 35

Optics 3 Question 35

35. An object is approaching a thin convex lens of focal length $0.3 m$ with a speed of $0.01 m / s$ . Find the magnitudes of the rates of change of position and lateral magnification of image when the object is at a distance of $0.4 m$ from the lens.

(2004, 4M)

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Answer:

Correct Answer: 35. $0.09 m / s, 0.3 / s$

Solution:

Differentiating the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ with respect to time, we get

$\begin{aligned} - \frac{1}{v^{2}} \cdot \frac{d v}{d t} + \frac{1}{u^{2}} \cdot \frac{d u}{d t} = 0 (as f = constant) \\ ∴ & \frac{d v}{d t} = \frac{v^{2}}{u^{2}} \cdot \frac{d u}{d t} \end{aligned}$

Further, substituting proper values in lens formula, we have

$\begin{aligned} \frac{1}{v} + \frac{1}{0.4} & = \frac{1}{0.3} (u = - 0.4 m, f = 0.3 m) \\ v & = 1.2 m \end{aligned}$

Putting the values in Eq. (i), we get

Magnitude of rate of change of position of image $= 0.09 m / s$

Lateral magnification, $m = \frac{v}{u}$

$\begin{aligned} ∴ \frac{d m}{d t} & = \frac{u \cdot \frac{d v}{d t} - v \cdot \frac{d u}{d t}}{u^{2}} = \frac{(- 0.4) (0.09) - (1.2) (0.01)}{(0.4)^{2}} \\ = - 0.3 / s \end{aligned}$

$∴$ Magnitude of rate of change of lateral magnification

$= 0.3 / s$

Optics 3 Question 35

35. An object is approaching a thin convex lens of focal length $0.3 m$ with a speed of $0.01 m / s$ . Find the magnitudes of the rates of change of position and lateral magnification of image when the object is at a distance of $0.4 m$ from the lens.

Answer:

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Optics 3 Question 35

35. An object is approaching a thin convex lens of focal length 0.3m with a speed of 0.01m/s. Find the magnitudes of the rates of change of position and lateral magnification of image when the object is at a distance of 0.4m from the lens.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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35. An object is approaching a thin convex lens of focal length $0.3 m$ with a speed of $0.01 m / s$ . Find the magnitudes of the rates of change of position and lateral magnification of image when the object is at a distance of $0.4 m$ from the lens.