An object is placed at a distance of 1.5 m from a screen and a convex lens is interposed between them. The magnification produced is 4. What is the focal length of the lens.
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To find the focal length of the lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens,
- v is the image distance from the lens, and
- u is the object distance from the lens.
Given that the magnification produced by the lens is 4, we can use the magnification formula:
magnification (m) = - v / u
where m is the magnification.
We have the magnification as 4, so we can rewrite the magnification formula as:
4 = -v / u
Simplifying, we get:
v = -4u
Now, we can substitute this value of v into the lens formula:
1/f = 1/(-4u) - 1/u
Simplifying further, we get:
1/f = -1/u
To find the focal length, we need to know the object distance (u) from the lens.
In the given problem, it is mentioned that the object is placed at a distance of 1.5 m from the screen. So, in this case, the object distance (u) is 1.5 m.
Substituting this value into the equation, we have:
1/f = -1/1.5
Simplifying,
1/f = -2/3
To find f, we can invert both sides of the equation:
f = 3/-2
Therefore, the focal length of the lens is -1.5m.
M= -di/do
solve for di.
then
1/f=1/di+1/do solve for f
m = 4
= v/u =4
v = 4u
then,
1/f = 1/v - 1/u
substitute v with 4u,
1/f = 1/4u - 1/u
1/f = 1/4u - 4/4u
1/f = -3/4u
=f=-4u/3
total dist,
u + 4u = 1.5 * 100 (m-cm)
5u = 150
u = 150/5 = 30cm
substituting u in -4u/3
-4 * 30/3
-120/3 = -40cm
hope so you got it
this might be the ans