An object is kept at a distance of 100 cm from a screen. A convex lens is to be placed in between such that image is formed on the screen and image size is four times the object size. Find the focal length of lens.
Answers
Answer:
Explanation:For a thin lens the following is true. Take care that i’m using positions instead of distances.
img-obj = f*(2-M-1/M)
Now we know that M=3 (what was meant is actually M=-3, else the object would be virtual and the lens negative = concave or the image would be virtual) and img-obj = 60cm.
Then we find f = 11.25cm with the given formula.
Also the following formulas hold true for thin lenses:
M = 1-(img-lens)/f
1/M = 1+(obj-lens)/f
Since the usually used p and q or u and v are either abs(img-lens) or abs(obj-lens) you can do the rest from here or see the solution in the picture below
The solution with a virtual object + concave lens would have looked like this:
The solution with a virtual image would use img-obj = - 60cm (that’s why signs are so important and it’s so weird that they are usually abandoned)
Given:
The distance between object and screen, i.e., (u + v) = 100 cm
Magnification, m = -4 (negative due to real image)
To Find:
The focal length of lens.
Calculation:
- As (u+v) = 100
⇒ v = 100 - u
- Magnification = v / u
⇒ m = (100-u) / u
⇒ -4 = (100/u) -1
⇒ u = - 100/3 cm
- Again, using the formula for magnification:
m = f / (f + u)
⇒ mf + mu = f
⇒ f = mu / (1-m)
⇒ f = {-4 × (-100/3)} / {1-(-4)}
⇒ f = (400/3) × 1/5
⇒ f = 80/3 cm
or f = 26.67 cm
- So, the focal length of lens is 26.67 cm.