1.
3TO FIND THE FOCAL LENGTH OF A CONVEX LENS BY PLOTTING GRAPHS BETWEEN
1 1
uAND pOR BETWEEN AND
Lens formula gives relationship between object distance (u), image distance (v) and focal length (). A graph bctween
1/u and 1/v is astraight line and intercepts of the graph gives the value of 1/f.
Aim
11
To find the focal length of a convex lens by plotting graphs between u andv or between and
Materials Required
" A convex lens of small focal length Two needles Three uprights
" Optical bench " Knitting needle " Metre scale
Clamp
PRACTICAL SKILLS IN PHYSICS-12 111
Theory
Focal length of a convex lens is calculated by using the formula:
or,
distant object. The image of distant object is forned
Approximate focal length of convex lens can be found by using a
at focus of a convex lens.
Procedure
Determining Approximate Focal
Length of Convex Lens IrmageAB of
Select a distant object which is in bright
light, e.g. a tall tree or an electric pole. A 2F Image
F needle
" Keep the lens in such a way that you 2F
CD
get an image of the distant object on a Object
needle
Screen or wall. AB
" Measure the distance between the lens lens
focal length of convex
and screen. This will give approximate Setup to determine the
focal length of the given convex lens.
Setting Up the Apparatus
horizontal position or not.
Select a rigid table. Check whether the table is in
" Keep the optical bench on the table.
" Place three uprights on the optical bench.
" Keep the convex lens on the middle upright. be at about one
convex lens. The distance between them should
Keep the object needle on the left side of the
and a half times the approximate focal length. them should be at more than
the convex lens. The distance between
Keep the image needle on the right side of
two times the approximate focal length.
Determination of Object and Image Distance
a real, inverted and magnified image beyond 2F.
Adjust the object needle and image needle so that you get
as shown in figure.
The image needle and image should be coincident;
the tip of the image.
" Ensure that the tip of the image needle touches
parallax error.
" Adjust the image needle so that there would be no
" Apply index correction by using a horizontal needle.
This is done to ensure that the tips of the object needle,
the same line.
image ncedle, image and O of the lens; all lie on
Determination of Focal Length
formula:
Focal length of the given convex lens can be calculated by using the following
f
u and v.
Ve Find the focal length for each set of observations for
respectively. From grap
. Plot a graph between u andyor 1/u and 1/v by taking them along X-axis and Y-axis
find the value of f.
Observations
Least count of meter scale
Cm.
Approximnate focal length of convex lensobserved distance =
Cm.
Index correction,e# actual distance-
Prscs-l2
PRACICAL SKLLSIN
112
Y
Graph between u and v
scale: Graph between 1/u and 1/v
-axis: 1 cm = cm.
Scale:
-axis: 1 cm = Cm.
X-axis 1 cm cm
yaxis :1cm = Cm
v.(cm) (cm1/v )
45 o X X
B
u (cm)
1/u (cm)
uVs v graph
1/uVs 1/v graph
Calculations
Focal length:
f= U-V
Mean of focal length:
f= 4
=...cm
Calculation of f from graph between u and v
" Choose a suitable but the same scale to represent u along X-axis and v along Y-axis.
" Plot the graph for different values ofu and v.
" Draw a line OA making an angle of 45° with either axis.
" Draw AB and AC perpendicular to X-axis and Y-axis respectively.
" Coordinates of point A must be (-2f. 2)
61 13 16.52
" So, AB = AC= 2f or 0C = OB = 2f
OB 61 13.42
Mean value of f= cm.
f=
2 5817 24.04
48-17
Calculation of f from graph between 1/v and 1/u 625 4 3
" Choose asuitable but some scale to represent 1/u along X'-axis and 1/v along Y-axis.
" Plot the graph for diferent values of 1/u and 1/v.
" Graph is a straight line and cut the two axes at OA and OB (which are intercepts on axes).
" Measure the distance OA and OB, So f OA OB
Mean value of f= Cm.
PRACICAL SKLLS IN PHYSICS-12 113
Precautions
" Properly level the optical bench. vertically on the optical bench.
mounted
" The uprights should be rigid and should be
" The aperture of convex lens should be small.
image needle.
" The tip of image should not overlap with the tip of of convex lens.
optical centre
" The tip of the needles should be in line with the
measuring object distance or image distance.
eye too close while
t keep your obiect distance and image distance.
to correctlv measure
OSe a horizontal needle
" The experiment should be conducted in a well lit room.
Sources of Error
" Incorrect levelling of optical bench.
the convex mirror.
Iips of object needle and image needle may not be in line with the pole of
" Possibility of parallax error.
" Uprights may not be in vertical position.
Suggested Experiment
1. Plot a graph between u -v and u + v. Find focal length by using this graph.
2. Plot a graph between
11
X- and
1 1
+-. Find the focal length using this graph.
VIVA VOCE
