1.- An object of 5 cm in height is 40 cm from a converging lens. It produces an inverted image which is found 30 cm from the lens. Find a) the focal length of the lens, b) the magnification, and c) the image height.
To find the focal length of the lens, you can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
In this case, the object distance (u) is given as 40 cm, and the image distance (v) is given as 30 cm.
a) Focal length (f):
1/f = 1/30 - 1/40
Simplifying the equation:
1/f = (4 - 3)/120
1/f = 1/120
Therefore, the focal length (f) of the lens is 120 cm.
b) Magnification (m):
The magnification (m) of the lens can be calculated using the formula:
m = -(v/u)
In this case, v = 30 cm and u = 40 cm.
m = -(30/40)
Simplifying the equation:
m = -3/4
Therefore, the magnification (m) is -3/4.
c) Image height:
The image height can be calculated using the magnification formula:
m = -h'/h
where h' is the image height and h is the object height.
In this case, the object height (h) is given as 5 cm.
-3/4 = -h'/5
Cross-multiplying:
-3 * 5 = -4 * h'
15 = -4 * h'
Simplifying the equation:
h' = -15/-4 = 3.75 cm
Therefore, the image height (h') is 3.75 cm.