Important Equations:

A negative magnification, which occurs when both o and i are positive,  

y' is the height of the image 

y is the height of the object 

i is image distance 

o is object distance

o is the object distance

i is the image distance 

f is the focal length

Types of lenses 

 Diverging lenses (Concave lenses)

Converging lenses (convex lenses) 

For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative. 

1.  The figure shows a thin converging lens of focal length 12 cm. A small object O (indicated by a vertical arrow) is placed on the principal axis of this lens at a distance of 10 cm from the optic centre of the lens.

(a) Making use of at least two rays proceeding from the object, draw a ray diagram showing the image formed by the lens.

(b) Comment on the nature of the image: whether it is real or virtual; magnified or diminished; erect or inverted.

Justify your comment.

(c) Another thin converging lens of focal lens 20 cm is kept in contact with the above lens so that they have a common principal axis. The object O is kept at 10 cm itself from the centre of the combination of these lenses. Calculate the distance of the image (formed by this combination) from the centre of the lens system, making use of the law of distances.

(d) Is the image formed in this case real or virtual? Justify your answer.



2.  A thin converging lens has a focal length of 10 cm. Calculation and construction of a ray diagram the position of the image of an object for the object distance so equal to  each of the following lenses, also describe whether the image is real or virtual, erect or inverted, magnified or diminished.

(a) 30 cm

(b) 15 cm

(c) 5.0 cm. 


2.  A thin diverging lens has a focal length of 10 cm. Find by (i) calculation and (ii) construction of a ray diagram the position of the image of an object for object distance equal to each of the following lenses 

(a) 30 cm

(b) 4 cm


3.An object 1.0 cm high is 100 cm from a converging lens. The inverted image is 3.0 cm high. Find the focal length of the lens.


4. When a person holds a magnifying glass 8.0 cm away from an object that is 2.0 cm wide, she sees a virtual image of the object, which is 6.0 cm wide. What is the focal length of the magnifying glass?