JEE Exam > JEE Questions > Show that a parallel bundle of light rays par...
Start Learning for Free
Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.?
Verified Answer
Show that a parallel bundle of light rays parallel to x-axis and incid...
Since it is parabolic with general equation
where
focal length
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
Show that a parallel bundle of light rays parallel to x-axis and incid...
Understanding the Problem:
A parallel bundle of light rays parallel to the x-axis is incident on a parabolic reflecting surface given by x=2by^2. We need to show that these rays converge to a single point called the focus of the reflecting surface.
Analysis of the Parabolic Reflecting Surface:
- The equation of the parabolic reflecting surface is x=2by^2, which is in the form of a parabola opening along the x-axis.
- The general equation of a parabola is x=4ay, where a is the focal length. By comparing this with x=2by^2, we can see that a=2b.
Deriving the Focus of the Reflecting Surface:
- The focus of a parabola is a fixed point where all the parallel rays converge after reflection.
- For a parabola opening along the x-axis, the focus is given by (a, 0). Since a=2b, the focus is located at (2b, 0).
Proving the Convergence of Light Rays:
- When parallel light rays parallel to the x-axis are incident on the parabolic reflecting surface, they follow the law of reflection and converge to the focus.
- Each ray reflects off the surface according to the angle of incidence equals the angle of reflection, eventually converging at the focus point.
Finding the Focal Length:
- The focal length of the parabolic reflecting surface x=2by^2 is given by a=2b.
- Therefore, the focal length of the reflecting surface is 2b.
A parallel bundle of light rays parallel to the x-axis is incident on a parabolic reflecting surface given by x=2by^2. We need to show that these rays converge to a single point called the focus of the reflecting surface.
Analysis of the Parabolic Reflecting Surface:
- The equation of the parabolic reflecting surface is x=2by^2, which is in the form of a parabola opening along the x-axis.
- The general equation of a parabola is x=4ay, where a is the focal length. By comparing this with x=2by^2, we can see that a=2b.
Deriving the Focus of the Reflecting Surface:
- The focus of a parabola is a fixed point where all the parallel rays converge after reflection.
- For a parabola opening along the x-axis, the focus is given by (a, 0). Since a=2b, the focus is located at (2b, 0).
Proving the Convergence of Light Rays:
- When parallel light rays parallel to the x-axis are incident on the parabolic reflecting surface, they follow the law of reflection and converge to the focus.
- Each ray reflects off the surface according to the angle of incidence equals the angle of reflection, eventually converging at the focus point.
Finding the Focal Length:
- The focal length of the parabolic reflecting surface x=2by^2 is given by a=2b.
- Therefore, the focal length of the reflecting surface is 2b.
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
Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.?
Question Description
Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.?.
Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.?.
Solutions for Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? 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 Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? defined & explained in the simplest way possible. Besides giving the explanation of
Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.?, a detailed solution for Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? has been provided alongside types of Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? theory, EduRev gives you an
ample number of questions to practice Show that a parallel bundle of light rays parallel to x-axis and incident on a parabolic reflecting surface given by x=2by^2, will pass through a single point called focus of the reflecting surface. Also find the the focal length.? 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup