# Angular magnification of flat and concave mirrors

• 4Phreal
In summary, the conversation discusses finding the angular size of an object viewed through a flat mirror and a concave mirror with a focal length of 39 cm. The solution involves calculating angles using trigonometry and using the equations m = θ/θ2 and M = h'/h = -q/p. The angular magnification of the concave mirror is also compared to the flat mirror. It is suggested to sketch the situation to check the results using geometry instead of relying solely on memorized equations.
4Phreal

## Homework Statement

(a) I hold a flat mirror 22.4 cm in front of my face. There is a freckle on my
face 1 mm in diameter. Find the angular size of the freckle on the image of my face as
viewed by my eye. (b) Repeat for a concave mirror which has a focal length of 39 cm.
(c) What is the angular magnification of the concave mirror, as compared to the flat
mirror?

m = θ/θ2
M=h'/h=-q/p
1/p+1/q=1/f

## The Attempt at a Solution

For part a: I figured that θ is the angle with the mirror in use, and θ2 is the angle when the object is placed at the nearpoint without the mirror. I assumed I was looking for θ, so I drew a triangle and did the arctan of 0.1cm/44.8cm to get 0.128 degrees as my answer. I'm not sure if that is correct.

For part b: I found q using 1/p+1/q=1/f, and it was -52.62650602 cm. I then calculated total distance, q+p = 52.62650602 cm + 22.4 cm = 75.02650602cm. Then using M=-q/p, i calculated the magnification to be 2.34939759, making h' 2.34939759 mm. Then to find theta, I did arctan(h'/totaldistance) to equal 0.179 degrees. Probably wrong.

Part c: I took angular size from part b and divided it by the angular size in part a because i figured that theta2 is the same for both.

Last edited:
Basically you have tried to remember how to use a bunch of memorized equations - so you are not sure you did it right. Have a go sketching the situation as a way of checking your results using geometry rather than rules.

## 1. What is angular magnification?

Angular magnification is the ratio between the angle subtended by an image formed by a lens or mirror and the angle subtended by the object being viewed.

## 2. How is angular magnification calculated for flat mirrors?

For flat mirrors, the angular magnification is equal to the ratio between the distance of the image from the mirror and the distance of the object from the mirror. This can be represented by the equation M = -di/do, where M is the angular magnification, di is the distance of the image from the mirror, and do is the distance of the object from the mirror.

## 3. How does the curvature of a mirror affect its angular magnification?

The curvature of a mirror affects its angular magnification because it determines the shape and size of the image formed. For convex mirrors, the image will always be smaller than the object, resulting in a magnification less than 1. For concave mirrors, the image can be larger or smaller than the object, depending on the position of the object relative to the focal point of the mirror.

## 4. Can angular magnification be negative?

Yes, angular magnification can be negative. This occurs when the image formed by a mirror is inverted compared to the object. In this case, the angular magnification will have a negative value.

## 5. How can angular magnification be used in practical applications?

Angular magnification is commonly used in telescopes and microscopes to magnify distant objects or small objects respectively. It is also used in optical instruments such as cameras and binoculars to produce a larger and clearer image of an object. Additionally, angular magnification is important in understanding the behavior of light and image formation in mirrors and lenses.

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