# A lens and a convex mirror problem

• zimo
In summary, for this problem, a body is positioned 40 cm from the left of a lens with a focal length of 30 cm, and the lens is positioned 100 cm left of a convex mirror with a radius of curvature of 60 cm. The image will be formed after the lens at a distance of 120 cm. The convex mirror will then interrupt the rays to form a real image, with a virtual object distance of 20 cm. The mirror can be considered either concave or convex to find the image distance.
zimo

## Homework Statement

A body is positioned 40 cm from the left of a lens (f=30) and the lens is positioned 100cm left of a convex mirror (|R|=60), where will be the image and what type and magnitude will it have?

1/u + 1/v = 1/f

## The Attempt at a Solution

I tried to calculate the image after the lens - and got v = 120 cm.

Now, I don't know how to interpret the answer.
Can anyone help me out on this?

Thanks

#### Attachments

• problem_3_10.png
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The convex mirror interrupt the rays to form the real image.
So (120 - 100) = 20 cm becomes the virtual object distance for the convex mirror. Now proceed.

That's my problem, now it is considered concave?

You can consider the mirror concave, and find the image distance that way, or you take it convex and use negative object distance.

ehild

Last edited:
for your question. Based on the given information, the image will be located 120 cm to the right of the convex mirror, as you have correctly calculated. This means that the image will be virtual, as it is formed on the same side of the lens as the object. The type of image formed by a convex mirror is always virtual and upright.

As for the magnitude of the image, it can be calculated using the magnification equation:

m = -v/u

Where m is the magnification, v is the image distance, and u is the object distance. Plugging in the values, we get:

m = -(120 cm)/(40 cm) = -3

This means that the image will be 3 times smaller than the object.

The image will be located 120 cm to the right of the convex mirror, and it will be a virtual, upright image with a magnitude of -3.

## 1. How does a convex lens and a convex mirror differ in their optical properties?

A convex lens and a convex mirror have opposite effects on light rays. A convex lens converges light rays towards a focal point, while a convex mirror diverges light rays away from a focal point.

## 2. What is the focal length of a lens and a convex mirror?

The focal length of a lens is the distance from the center of the lens to the focal point, where light rays converge or diverge. For a convex mirror, the focal length is the same as the distance from the center of the mirror to the focal point, where light rays appear to originate from.

## 3. How do you calculate the magnification of a lens and a convex mirror?

The magnification of a lens is calculated by dividing the image distance by the object distance. For a convex mirror, the magnification is equal to the negative of the image distance divided by the object distance.

## 4. Can a lens and a convex mirror be used together in an optical system?

Yes, a lens and a convex mirror can be used together in an optical system. The lens can be placed in front of the mirror to correct the image formed by the mirror and provide a larger field of view.

## 5. How does the curvature of a lens and a convex mirror affect their optical properties?

The curvature of a lens and a convex mirror determines the amount of bending of light rays and the focal length of the optical system. A steeper curvature results in a shorter focal length, while a flatter curvature results in a longer focal length.

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