# Magnification/Focal Length

• matt72lsu
In summary: This is where you imagine a ray coming from the bulb and going to the mirror. Then you work out the distance from the mirror to the beam ( bulb). The focal length of the mirror is the distance from the mirror to the end of the beam.

## Homework Statement

Shaving/makeup mirrors typically have one flat and one concave (magnifying) surface. You find that you can project a magnified image of a lightbulb onto the wall of your bathroom if you hold the mirror 2.0 m from the bulb and 3.7 m from the wall.

a) What is the magnification of the image?
b) Is the image erect or inverted?
c) What is the focal length of the mirror?

m = - di/do ?
1/di +1/di = 1/f

## The Attempt at a Solution

I'll be honest, I have no clue how to start this problem. Any help would be appreciated

Ok thanks! as far as magnification, is the formula i provided correct? and how do i figure out if it is inverted or not?

The positive or negative signs in the equations have the following significance

(from further down in the link I gave you)

• f is + if the mirror is a concave mirror
• f is - if the mirror is a convex mirror
• di is + if the image is a real image and located on the object's side of the mirror.
• di is - if the image is a virtual image and located behind the mirror.
• hi is + if the image is an upright image (and therefore, also virtual)
• hi is - if the image an inverted image (and therefore, also real)

hi is height of image, ho is height of object

The formula for these is
magnification = hi/ho = -di/do

Just keep a close eye on the negative sign in the equation and be consistent with signs generally, and this will tell you if the image is real and inverted; or virtual and erect.

The other way of working this out is to draw a ray diagram.

## What is magnification?

Magnification is the ratio of the size of an object as viewed through a lens to its actual size. It is typically expressed as a decimal or percentage.

## How is magnification calculated?

Magnification is calculated by dividing the image size by the object size. For example, if the image size is 10mm and the object size is 2mm, the magnification would be 5x (10/2 = 5).

## What is focal length?

Focal length is the distance between the lens and the image sensor when an object is in focus. It affects the field of view and magnification of the image.

## How does focal length affect magnification?

The longer the focal length, the higher the magnification. This means that objects will appear larger when viewed through a lens with a longer focal length compared to a shorter focal length.

## What is the difference between optical and digital magnification?

Optical magnification is achieved through the use of lenses and does not degrade the image quality. Digital magnification is achieved by cropping or enlarging an image digitally, which can result in loss of image quality.