This document provides information about refraction of light at curved surfaces and lenses. It defines key terms like radius of curvature, principal axis, focal length. It describes the properties and image formation characteristics of convex and concave lenses. The lens formula and lens maker's formula are provided. Multiple choice questions at the end test the understanding of concepts like image formation by lenses and mirrors, properties of convex, concave and plane mirrors, and characteristics of lenses.

1. Chapter 6
Refraction of light at Curved Surfaces
Summary:
Consider a curved surface which is a part of a sphere.
The centre of the sphere, is called centre of curvature.
The centre of curved surface is called the pole (P) of curved surface. The line
that joins the centre of curvature and the pole is called ‘principal axis’. It is
denoted by letter ‘C’.
Formulae: n2 /v – n1/u = (n2-n1)/R
Where n1, n2 = the refractive indices of two material media of curved surfaces,
u = object distance, v = image distance, and R = Radius of curvature
The above formula for plane interface in refraction is given by:
n2 /v – n1/u = 0
or n2 /v = n1/u
Focus or focal point:
The point of convergence (or) the point where the rays appear to be emanating is
called Focus(F) or focal point.
Every lens has two focal points.
The distance between optic centre and focal point is called “focal length (f)”
The focal points are equidistant from the centre, ie pole of the lens.
The distance between two focal points = 2F1 = 2F2 = Twice the focal length.

2. When a light ray incident on a lens:
1. A ray is undeviated when passes through principal axis.
2. A ray is undeviated when it passes through the optic centre.
3. The rays travelling parallel to principal axis converge at the focus or
diverge from the focus.
4. The light rays obey the principle of least time.
5. The ray passing through the focus after refraction will take a path
parallel to principal axis.
Lenses:
• A lens is made up of transparent material.
• Bounded by two surfaces both or one is spherical surface.
• ‘A lens is bounded by atleast one curved surface’.
• Lenses are of various types.
Convex Lens:
• It may have two spherical surfaces bulging outside.
• It is called double convex lens or biconvex lens.
• It is thick at the middle and thin at the edges.
Concave lens:
• A double concave lens has two spherical surfaces.
• It is thin at middle and thick at the edges.
• Each curved surface of a lens is a part of a sphere.
Centre of curvature:
• It is the centre of sphere contains lens part.
• It is denoted by C.

3. • The distance between curved surface and centre of curvature
is called “radius of curvature (R)”.
• If the lens contains two curved surfaces, it will have two
centres of curvatures namely C1 and C2 .
• The line joining between two centres is called principal
axis.
• The mid point of the lens is called optic centre(P).
Image Positions of Convex Lens for various positions of object:
✓ Object at infinity: A point sized image at focal point will be
formed.
✓ Object beyond the centre of curvature of Principal axis: Image
will be real, inverted and diminished formed on principal axis
between the points F1 and 2F1.
✓ Object at the centre of curvature (at 2F2): The image will be on
another side at 2F1, and a real, inverted and of same size as the
object.
✓ Object between Centre of curvature (2F2) and Focal point(F2):
The image will be beyond 2F1 which is real, inverted and
magnified.
✓ Object at focal point (F2): Image at infinity.
✓ Object between Focus (F1) and optic centre: Image on the
same side.
• Virtual, erect and magnified which can be seen with
eyes.
• Cannot be caught on the screen.
• This behaviour of Convex lens is useful to construct a
microscope.

4. For concave lens: The image will be always erect, virtual and
diminished in size, irrespective of the position of
object.
Lens formula:
1/v - 1/u = 1/f
For any lens with sign convention.
✓ Focal length of a lens depends upon the surrounding medium.
✓ Focal length of lens increases in water.
Lens maker’s formula: In the air medium, the relative refractive index is
the absolute refractive of the lens,
1/f = (n -1)( 1/R1 – 1/R2 )
Where R1 and R2 are radii of curvature, n is the
This is called lens maker’s formula.
Note: Always use sign convention.
✓ If the refractive index of the medium is less than convex
lens, behaves as a convergent lens.
✓ Convex lens behaves as a divergent lens, if the refractive
index of the transparent medium is greater than lens.
✓ Air bubble in water behaves as a diverging lens.
Multiple choice questions:
1. The rays from the distant object falling on the convex lens pass through
[ ]
a) Focus b) centre of curvature c) Pole d) Radius of curvature
2. What is the focal length of the plano convex, when R is the radius of the
curvature of the surface, n is the refractive index of the lens? [ ]
a) f = R b) f = R/2 c) f = R/(n-1) d) f = (n-1)/R

5. 3. Real or virtual image is formed by which of the following lenses? [ ]
a) Bi convex lens b) Biconcave lens c) Plano convex mirror d) all of
these
4. The value of the focal length of the lens is equal to the value of the image
distance when the rays are [ ]
a) Passing through the optic centre b) parallel to the principal axis
c) Passing through the focus d) In all these cases
5. Which of the following is the lens maker’s formula
a) 1/f = (n-1) (1/R1 + 1/R 2) b) 1/f = (n + 1) (1/R1 – 1/R2 )
c) 1/f = (n - 1) (1/R1 – 1/R2) d) 1/f = (n + 1) ( 1/R1 + 1/R2)
Questions on Concave Mirrors:
6. The image formed by concave mirror when the object is held at a
distance less than the focal length, is [ ]
a) Erect b) virtual and inverted c) inverted d) None
7. The property of which mirror when the object is held close less than
the focal length is used as a shaving mirror [ ]
a) plane mirror b) convex mirror c) concave mirror d) none
8. A mirror used by dentists is [ ]
a) concave mirror b) convex mirror c) Plane mirror d) None
9. Which mirror focuses the parallel sun rays at the focal point of the
mirror [ ]
a) convex mirror b) concave mirror c) Any mirror d) plane mirror
10. Solar cooker works on the property of which mirror? [ ]
a) plane mirror b) convex mirror c) concave mirror d) none
11. Archimedes burnt the ships using which property of concave mirror?
[ ]
a) Parallel rays converge at focal point of the mirror b) Parallel rays
diverge from pole c) Deviated from centre of curvature after reflection

6. d) None of the above.
12. Watchmaker uses _____________ to repair.
a) Convex mirror b) concave mirror c) concave lens d) convex lens
13. Pick the correct answer from the following two answers: [ ]
1) Focal length of a lens depends on the surrounding medium.
2) Focal length of a lens changes with object distance.
a) both (1) and (2) are true b) both (1) and (2) are false
(c) Only (1) is true (d) Only (2) is true
14. The size of the image formed by a convex lens is same as that of
the object, when the object is placed [ ]
a) At the centre of curvature b) Between the centre of curvature
and focus c) Beyond the centre of curvature d) Between focus
and centre.
15. The lens, which is thin, at the middle on both sides and thicker, at
the edges is [ ]
a) bi- convex b) concavo- convex c) plano – convex d) bi -
concave
16. If 40 cm each is the object and image distances respectively for a
convex lens, then the focal length is [ ]
a) 80 cm b) 40 cm c) 20 cm d) 25 cm
KEY
1. a 2. c 3. a 4. c 5. c 6. a 7. c 8. a 9. b 10. c
11. a 12. d 13. c 14. a 15. d 16. c