Image formation by lens

Image formation by lens

Introduction : From lens formula, we find that for a lens of a fixed focal length as object distance u changes, image distance n also changes. Moreover, as u decreases or increases, this changes the position, the nature and the size of the image.

Different cases, are as given below with their ray diagrams.

Convex Lens in different cases

Case 1 : Object at Infinity

A point object lying on the principal axis

Rays come parallel to the principal axis and after refraction from the lens, actually meet at the second principal focus F2.

 

A point object lying on the principal axis
A point object lying on the principal axis

Fig. Convex lens point object at infinity, image at focus.

The image is formed at focus F2. It is real and point sized.

A big size object with its foot on the principal axis

Parallel rays come inclined to the principal axis. Image of foot is formed at the focus.

Image is formed at the second principal focus F2. It is real inverted and diminished (smaller in size than the object). (Fig.)

Fig. Convex lens : big size object at infinity, image at focus

Case 2 : Object at distance more than twice the Focal Length

Real object AB has its image A¢B¢ formed between distance f and 2f.

The image is real inverted and diminished (smaller in size than the object)

Fig. Convex lens : object beyond 2f, image between f and 2f.

Case 3. Object at distance twice the Focal Lengths

Real object AB has its image A¢B¢ formed at distance 2f.

Fig. Convex lens : object at distance 2f, image at distance 2f.

The image is real, inverted and has same size as the object.

Case 4 : Object at distance more than Focal Length and less than twice is Focal Length

Real object AB has its image A¢B¢ formed beyond distance 2f.

Fig. Convex lens : object at distance between f and 2f, image beyond 2f.

The image is real inverted and enlarged (bigger in size than the object).

Case 5 : Object at Focus

Real object AB has its image formed at infinity.

Fig. Convex lens : object at focus, image at infinity.

The image is imaginary inverted (refracted rays to downward) and  must have very large size.

Case 6 : Object between Focus and Optical Centre

Real object AB has its image A¢B¢ formed in front of the lens.

Concave lens in different cases

Case 1 : Object at infinity

A point object lying on the principal axis.

Rays come parallel to the principal axis and after refraction from the lens, appears to come from the second principal focus F2.

Fig. Concave lens point object at infinity, image at focus.

The image is formed at focus F2. It is virtual and point sized (fig.)

A big size object with its foot on the principal axis.

Parallel rays come inclined to the principal axis. Image of foot is formed at focus.

The image is formed at the second principal focus F2.

It is virtual–erect and diminished (fig.)

Fig. Concave lens : big size object at infinity image at focus.

Case 2 : Object at a Finite Distance

Real object AB has its image A′B′ formed between second principal focus F2 optical centre C.

The image is virtual–erect and diminished.