SATHEE: Optics 1 Question 11

Optics 1 Question 11

11. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

(2018 Adv.)

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Answer:

Correct Answer: 11. (d)

Solution:

Image of point $A$

$\frac{P Q}{x} = \frac{A B}{f / 2} \Rightarrow P Q = \frac{2 (A B) x}{f}$

For $A$ :

$\frac{1}{v} + \frac{1}{[- (f / 2)]} = \frac{1}{- f} \Rightarrow v = f$

$\begin{array}{cc} \Rightarrow & \frac{I_{A B}}{A B} = - \frac{v}{u} = - \frac{f}{- \frac{f}{2}} \\ \Rightarrow & I_{A B} = 2 A B \end{array}$

For height of $P Q$ ,

$\begin{aligned} \frac{1}{v} + \frac{1}{- [(f - x)]} = \frac{1}{- f} \\ \Rightarrow \frac{1}{v} = \frac{1}{(f - x)} - \frac{1}{f} \Rightarrow v = \frac{f (f - x)}{x} \\ \Rightarrow \frac{I_{P Q}}{P Q} = - \frac{v}{u} = \frac{f (f - x)}{x [(f - x)]} = \frac{f}{x} \\ \Rightarrow I_{P Q} = \frac{f}{x} P Q = \frac{f}{x} \frac{2 (A B) x}{f} ∵ P Q = \frac{2 (A B) x}{f} \\ I_{P Q} = 2 A B \end{aligned}$

(Size of image is independent of $x$ . So, final image will be of same height terminating at infinity.)

Optics 1 Question 11

11. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

Answer:

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Optics 1 Question 11

11. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

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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11. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)