# How to Calculate Radii for a Symmetric Converging Lens to Double Image Size?

• Mennethitus
In summary, the question asks for the radii of a symmetric converging plastic lens that will form an image on a screen twice the height of an object placed 34.0 cm away. The problem can be solved using the equations (1/f) = (1/s) + (1/s') and (1/f) = (n-1)[(1/R)-(1/R')]. The correct answers are not 71.5 and 25.2 as attempted, and the index of refraction of plastic is given as 1.59. The problem was eventually solved by the person asking for help.
Mennethitus

## Homework Statement

An object is 34.0 cm from a screen.

What are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object? (Take the index of
refraction of plastic to be 1.59.)

## Homework Equations

(1/f) = (1/s) + (1/s')

(1/f) = (n-1)[(1/R)-(1/R')]

## The Attempt at a Solution

I attempted to use those two equations to solve the problem, my answers were 71.5 and 25.2. Both were wrong.

If anyone can help within the next 1 hour and 30 minutes I would really appreciate it, thank you

Never mind, I solved it.

!

I would suggest reviewing your calculations and equations to ensure accuracy. Additionally, double check the units and make sure they are consistent throughout the problem. It may also be helpful to draw a diagram to visualize the problem and identify any potential errors. If you are still having trouble, I recommend seeking assistance from a teacher or classmate. Remember to always check your work and approach problems systematically to ensure the correct solution. Good luck!

## 1. What is a biconvex lens and how does it work?

A biconvex lens is a type of lens with two convex surfaces. It works by refracting, or bending, light rays as they pass through the lens. The convex shape of the lens causes the light rays to converge, creating a magnified, inverted image of the object being viewed.

## 2. What is the difference between a biconvex lens and a plano-convex lens?

A plano-convex lens has one flat (plano) surface and one convex surface, while a biconvex lens has two convex surfaces. This difference affects the way light is bent and the resulting image produced by the lens.

## 3. What is the focal length of a biconvex lens?

The focal length of a lens is the distance from the center of the lens to the point where light rays converge or appear to originate from. For a biconvex lens, the focal length is equal to half of the radius of curvature of the lens surfaces.

## 4. How do you calculate the power of a biconvex lens?

The power of a lens is measured in diopters (D) and is equal to the reciprocal of the focal length in meters. For a biconvex lens, the power can be calculated by dividing the refractive index of the lens material (n) by the focal length (f): Power (D) = n / f.

## 5. What are some common uses for biconvex lenses?

Biconvex lenses are commonly used in optics and imaging systems, such as cameras, telescopes, and microscopes. They are also used in corrective eyewear, such as glasses and contact lenses, to help improve vision for people with conditions like nearsightedness or farsightedness.

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