# Lenses - Thin-Lens Equation and Magnification Equation

• missmia
In summary, the conversation discusses a problem involving a camera with two interchangeable lenses and a woman's height. The problem requires the use of the thin-lens equation and magnification equation to determine the height of the woman's image on the film for both a 35.0 mm lens and a 150.0 mm lens. The attempted solution involves converting units and using the equations, but there is an error in the calculation due to incorrect unit conversion. The conversation concludes with the error being pointed out and corrected.
missmia
[SOLVED] Lenses - Thin-Lens Equation and Magnification Equation

I can't figure out what I am doing wrong, your help would be greatly appreciated :)

Here is the Homework Problem

A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and 150.0 mm. A woman whose height is 1.80 m stands 9.00 m in front of the camera. What is the height (including sign) of her image on the film, as produced by each of the following.
(a) the 35.0 mm lens
(b) the 150.0 mm lens

ATTEMPTED SOLUTION:

$$\frac{1}{d_{i}}$$ = $$\frac{1}{.0035m}$$ - $$\frac{1}{9.0m}$$

which gives $$d_{i}$$ = .003501m

then, I used the magnification equation: m = - $$\left[\frac{.003501m}{9.0m}\right]$$ = -3.89 x $$10^{-4}$$x

then, I used $$h_{i}$$ = m$$h_{o}$$ = -3.89 x $$10^{-4}$$ x 1.80m = -7.00 x $$10^{-4}$$

Be careful with the units. remember 35mm is 3.5cm which is 0.035m.

oh gosh! I can't believe I didn't notice that. Thanks again :)

## 1. What is the thin-lens equation and how is it used?

The thin-lens equation is a mathematical formula that relates the distance of an object from a thin lens, the distance of the image from the lens, and the focal length of the lens. It is used to calculate the position and size of an image formed by a thin lens.

## 2. How do you determine the magnification of an image formed by a thin lens?

The magnification of an image formed by a thin lens can be determined by using the magnification equation, which is the ratio of the height of the image to the height of the object. It can also be calculated by dividing the image distance by the object distance.

## 3. What is the difference between a converging and a diverging lens?

A converging lens, also known as a convex lens, has the ability to bring parallel light rays closer together and form a real image. A diverging lens, also known as a concave lens, has the opposite effect and spreads out parallel light rays, creating a virtual image.

## 4. Can the thin-lens equation and magnification equation be used for any type of lens?

Yes, the thin-lens equation and magnification equation can be used for any type of lens as long as the lens is thin and the object is located far enough from the lens so that the lens can be treated as a single point.

## 5. How does changing the distance of the object from a thin lens affect the image?

Changing the distance of the object from a thin lens can affect the size and position of the image. When the object is moved closer to the lens, the image will become larger and move further away from the lens. When the object is moved further away from the lens, the image will become smaller and move closer to the lens.

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