Calculations Calculate the reciprocal of the object distance
Tabulation of Data Table 13.6
u / cm v / cm
1 / cm1 u
1 / cm1 v
Graph Plot a graph of the inverse of object distance , measured in cm1, against the inverse of image distance ,
a
1 u b
measured in cm1, with the inverse of image distance on the y-axis. Extend the line of best fit so that it cuts the x-axis and y-axis. Conclusion
The line should cut both axes at the same value.This value is equal to the inverse of the focal length a Based on the equation
When the line cuts the x-axis y = 0, which means v 1
1 u 1
f
1 v 0
, since a we get, it is clear that
1 v b
1 f b
is plotted on the y-axis.2
1 v 0
implies
1 f 1
u the x coordinate where
the line cuts the x-axis. It is equally valid to choose the y coordinate where the line cuts the y-axis as this is where
1 u 0
Take care when using the metre stick to avoid parallax error. Measure distance from the screen to the centre of the lens. Take care to find the sharpest image on the screen. Repeat a number of times at each value of u and find an average v.
.
Precautions Carry out procedure to find approximate focal length.This will make it easier to find the exact image later. It will allow you to place the ray box outside the focal length which is necessary to produce a real image.
. Invert
this value to get the focal length (f ) of the lens.The focal length can be expressed in centimetres or metres. Explanation
a
1 v b
a
1 u b
and image distance . a
1 v b
2Strictly speaking, approaches 0 as
1 v
1 v = 0Q1 = 0 * vQ1= 0
1 f = 1
u + 1 v as
; obviously this cannot happen. By extending the
line of best fit so that it cuts the axes we get a very accurate approximation of as approaches 0. Another way of interpreting the graph is to rewrite the formula
1 f
1 v = 1
graph represents a line with slope –1 which cuts the y-axis at .1 f
