JEE Exam > JEE Questions > The image of the object formed by a convex sp...
Start Learning for Free
The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature?
Most Upvoted Answer
The image of the object formed by a convex spherical mirror is magnifi...
Explanation:
Let the distance between the object and the mirror be u, and the distance between the image and the mirror be v. The magnification produced by the mirror is given by
m = v/u
The magnification of the image formed by the mirror is one-third that of the object, so we have
v/u = 1/3
When the mirror is displaced by 40 cm along its principal axis in the direction of the light, the distance between the object and the mirror becomes u' = u + 40 cm, and the distance between the image and the mirror becomes v' = v + 40 cm. The magnification produced by the mirror is still given by
m' = v'/u'
The magnification of the image formed by the mirror after displacement is again one-third that of the object, so we have
v'/u' = 1/3
Substituting the values of v/u and v'/u' in these equations, we get
v/u = 1/3
v'/(u + 40) = 1/3
Solving these equations for v and v', we get
v = u/3
v' = (u + 40)/3
Substituting these values in the mirror formula 1/v + 1/u = 1/f, we get
1/(u/3) + 1/u = 1/f
1/(u+40)/3 + 1/u+40 = 1/f
Simplifying these equations, we get
f = -120 cm
The negative sign indicates that the mirror is convex. Therefore, the radius of curvature of the mirror is given by
R = 2f = -240 cm.
Let the distance between the object and the mirror be u, and the distance between the image and the mirror be v. The magnification produced by the mirror is given by
m = v/u
The magnification of the image formed by the mirror is one-third that of the object, so we have
v/u = 1/3
When the mirror is displaced by 40 cm along its principal axis in the direction of the light, the distance between the object and the mirror becomes u' = u + 40 cm, and the distance between the image and the mirror becomes v' = v + 40 cm. The magnification produced by the mirror is still given by
m' = v'/u'
The magnification of the image formed by the mirror after displacement is again one-third that of the object, so we have
v'/u' = 1/3
Substituting the values of v/u and v'/u' in these equations, we get
v/u = 1/3
v'/(u + 40) = 1/3
Solving these equations for v and v', we get
v = u/3
v' = (u + 40)/3
Substituting these values in the mirror formula 1/v + 1/u = 1/f, we get
1/(u/3) + 1/u = 1/f
1/(u+40)/3 + 1/u+40 = 1/f
Simplifying these equations, we get
f = -120 cm
The negative sign indicates that the mirror is convex. Therefore, the radius of curvature of the mirror is given by
R = 2f = -240 cm.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature?
Question Description
The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature?.
The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature?.
Solutions for The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? defined & explained in the simplest way possible. Besides giving the explanation of
The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature?, a detailed solution for The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? has been provided alongside types of The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? theory, EduRev gives you an
ample number of questions to practice The image of the object formed by a convex spherical mirror is magnified one third in comparison with the onject, if the mirror is displaced by 40 cm along ints principal axis in the direction of light, the image is again found one third in comparidon with the object. Find the radius of curvature? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup