Linear Magnification (m)

Magnification is the process of enlarging something’s apparent size rather than its actual size. The amount of enlargement is expressed as a numerical value called “magnification.” When this number is less than one, it indicates a size reduction, also known as minification or de-magnification. Furthermore, this notion has two variations. The first is through a microscope (which magnifies small objects), and the second is through a telescope that enlarges the view of a distant object, making it look closer and more distinct. The formula for magnification by mirror and lens is different, but the notion is the same.

What is Linear Magnification?

The relative amount to which the image of an item is amplified with regard to the object size is determined by the magnification generated by a spherical mirror. It is calculated as the ratio of the image’s height to the object’s height. The letter m is used to signify magnification. The magnification power of a lens refers to how much larger an image may look when seen through it. The focal length of the lens and the shortest distance of clear vision have a direct relationship.

Mirror Magnification

If the object’s height is h and the image’s height is h′, the magnification m produced by a spherical mirror is given by

 m = Height of the image (h’) / Height of the object (h )   

m = h′/ h 

The object distance (u) and image distance (v) are also connected to magnification (m). It can also be written as:

Magnification (m) = h’/h =  –  v/ u 

If an object is positioned above the principal axis, its height is assumed to be positive. For virtual pictures, the image height should be considered positive. For real-life images, however, it should be seen as a negative. A negative sign in the magnification value shows that the image is actual. A positive sign in the magnification value implies that the image is virtual.

For spherical mirrors, if the magnification (m) is- 

(i) Linear magnification, m > 1 indicates that the image is larger than the object.

(ii) Linear magnification, where m = 1 indicates that the image is the same size as the object.

(iii) m < 1 indicates that the image is reduced, meaning smaller than the real.

Example- What magnification is achieved in the case of a concave mirror if the image distance is 4cm and the object is positioned at 8cm?

As we all know, magnification may be determined using the method below:

Magnification (m) = h’/h =  –  v/ u 

Given, v= -4cm and u= -8cm the signs are given using sign convention.

m= -4/-8

m = -0.5 cm

As a result, there is a reduction of 0.5.

Lens Magnification

The magnification produced by a lens, such as that produced by spherical mirrors, is defined as the image height to object height ratio. The letter m is used to signify magnification. When using a convex lens, the magnification for actual and inverted pictures is always –ve, whereas the magnification for virtual and erect images is always +ve.

If h is the object’s height and h′ is the height of the image generated by a lens, then the lens’ magnification is given by, 

m = Height of the Image/ Height of the object 

m = h’/ h 

The object-distance u and the image-distance v are also connected to the magnification generated by a lens. This connection is established through

Magnification (m ) = h′/h = v/u

When determining the magnification for spherical mirrors, keep the following points in mind-

• The presence of a virtual and erect image is indicated by the positive magnitude or value of the magnification.
• The magnification’s negative magnitude or value suggests forming a real and inverted image.

Uses of Magnification

• A precision magnifier is similar to a regular magnification, but it contains many parts that work together to eliminate aberrations and give us a crisper image.
• A simple magnifier, a tiny water droplet, magnifies the thing in front of it. Due to the action of surface tension, water condenses into tiny spherical droplets. When a water droplet comes into touch with an item, it takes on a deformed spherical shape that can make an excellent picture of the object.

Conclusion

It refers to the process of using lenses to enlarge an item visually. Furthermore, the thing does not grow in size but merely looks to grow in size. Physically, understanding magnification is simple, and everyone can perceive it. Furthermore, we know how large or small the picture of the object will be. Microscopes, binoculars, and telescopes all magnify objects by utilising the unique properties of light-transducing lenses of various shapes. The magnification formula is the height of the image divided by the height of the object. Furthermore, the letter’  m’ signifies the object’s magnification.