Answer:
80mm or 8cm
Explanation:
According to the lens formula,
1/f = 1/u+1/v
If the object distance u = 4cm = 40mm
Object height = 1.5mm
Image height = 3mm
First, we need to get the image distance (v) using the magnification formula Magnification = image distance/object distance = Image height/object height
v/40=3/1.5
1.5v = 120
v = 120/1.5
v = 80mm
The image distance is 80mm
To get the focal length, we will substitute the image distance and the object distance in the mirror formula to have;
1/f = 1/40+1/-80
Note that the image formed by the lens is an upright image (virtual), therefore the image distance will be negative.
Also the focal length of the converging lens is positive. Our formula will become;
1/f = 1/40-1/80
1/f = 2-1/80
1/f = 1/80
f = 80mm
The focal length of the lens 80mm or 8cm
Answer: f = 4cm
Explanation: The lateral magnification formulae is given as
m = height of image /height of object or
m = - (image distance) /(object distance)
Image height (Hi) = 3mm, object height (Hob) = 1.5mm, object distance (u) =?, image distance (v) = - 4cm... The reason we have a negative image distance is because the image is upright and an upright image (aka virtual image) has negative image distance because the the refracting ray is on the opposite side of the image.
m = Hi/Hob
m = 3/1.5 = 2.
Since m =2, and v = - 4cm, we can get 'u' as follows
m = - v/u
2 = - (-4)/u
2 = 4/u
2u = 4, u = 4/2, u = 2cm.
Using the lens formulae
1/u + 1/v = 1/f
1/2 - 1/4 = 1/f
0.5 - 0.25 = 1/f
0.25 = 1/f
f = 1/ 0.25
f = 4cm
