Lenses 2

CALCULATIONS USING THE LENS FORMULA

fvu

111

Calculate the distance of the image to the converging lens in the following situations

object distance /cm Focal length /cm

a 30.0 40.0

b 25.0 20.0

c 50.0 20.0

d 40.0 40.0

In each case say whether the image is real or virtual

fvu

111

vuf

111

v

1

30

1

40

1

120

431 v

120

11 v

V= -120 cm

The image is 120 cm from the lens and it is virtual (- sign)

object distance /cm

Focal length /cm

Image dist ance cm

a 30.0 40.0 -120 (virtual)

b 25.0 20.0 100 (real)

c 50.0 20.0 33.3cm (real)

d 40.0 40.0 No image (rays emerge parallel)

Solved Example

The power of a lens

f

1

By definition the power of a lens is the reciprocal of its focal length in metres:

Lens power

This of course also means that the power of a lens is given by:

vu

11

Calculations With Lens Power

object distance /cm

Image distance/cm Focal length /cm

40.0 30.0

30 -120

20.0 50.0

20.0

Calculate the power of each of these lenses.

Determination Of The Focal Length Of A Converging Lens

The distant object method:

To make a rough estimate of the focal length of a convex lens. Produce a sharply illuminated image of a distant object (e.g. a distant window).

To a rough approximation the rays of light from the object will be arriving parallel at the screen and therefore the distance between the lens and the screen is approximately the focal length of the lens.

Lens formula method

• Using an illuminated object (O) change u, systematically measuring the distance v in each case

O

uv

A graph of 1/v against 1/u is plotted

1/u

m-1

1/v m-1

1/v= 1/f

1/u= 1/f fvu

111Because of the relationship

Where 1/u falls to zerofv

11

Extrapolate the line to meet the x and y axes

Where 1/v falls to zerofu

11