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Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta?
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Radius of curvature of a concave convex lens are 40cm 20cm shown to co...
Calculation of Beta
Given data:
- Radius of curvature of concave side, R1 = -40 cm
- Radius of curvature of convex side, R2 = 20 cm
- The convex side is silvered to a distance x on the principal axis
- The image is created on the object itself
Let the distance of the object from the lens be u.
Using the lens formula, 1/f = 1/v - 1/u, where f is the focal length and v is the distance of the image from the lens, we get:
f = (R2 * R1) / (R1 + R2) = -13.33 cm
Using the mirror formula, 1/f = 1/v + 1/u, where f is the focal length and v is the distance of the image from the mirror, we get:
f = x / 2
Equating the two values of f, we get:
x = -26.67 cm
The negative sign indicates that the image is formed on the same side as the object.
Now, using the magnification formula, m = -v/u = 1, where m is the magnification, we get:
v = u
Using the lens formula again, we get:
1/f = 1/u + 1/u
u = 2f = -26.67 cm
The negative sign indicates that the object is located to the left of the lens.
Finally, using the definition of beta, we get:
beta = u/x = 1.5
Explanation
Given the radius of curvature of the concave convex lens and the distance at which the convex side is silvered on the principal axis, we need to find the value of beta, where an object is placed so that its image is created on the object itself. To do this, we need to use the lens formula, mirror formula, and magnification formula. The lens formula relates the distance of the object and image from the lens to the focal length of the lens. The mirror formula relates the distance of the object and image from the mirror to the focal length of the mirror. The magnification formula relates the size of the object and image to their distances from the lens or mirror. By equating the focal lengths of the lens and mirror, we can find the distance at which the image is formed. Using the magnification formula, we can then find the value of beta.
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Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta?
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Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta?.
Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radius of curvature of a concave convex lens are 40cm 20cm shown to convex side is silvered to distance x on the principal axis where an object is placed so that its image is created on the object itself is given as 4 beta and the value of beta?.
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