A girl want to know the distance of a tree from where the point R where she is standing ,she used a convex lens to project the image of the tree onto a wall of 15M away ,she later moved the lens toward the tree and found that the image is again projected on the wall after moving 20M . Calculate the distance of the tree from the point to R.
To calculate the distance of the tree from point R, we can make use of the lens formula. The lens formula states that:
1/f = 1/v - 1/u,
where:
f = focal length of the lens,
v = distance of the image from the lens,
u = distance of the object from the lens.
We can consider the lens as telephoto (converging) since it is projecting a real image onto the wall.
Let's break down the given information:
1. The distance between the wall and the lens is 15 meters. We can call this v1.
2. When the girl moves the lens towards the tree, she finds that the image is again projected on the wall after moving 20 meters. We can call this v2.
3. The distance between the girl's position (point R) and the lens is the unknown value we need to find. We can call this u.
Now, we apply the lens formula for both situations:
For the first situation:
1/f = 1/v1 - 1/u.
For the second situation:
1/f = 1/v2 - 1/u.
We notice that the focal length f is the same in both situations. Therefore, we can equate the two equations:
1/v1 - 1/u = 1/v2 - 1/u.
By simplifying and rearranging the equation, we get:
1/u = 1/v1 - 1/v2.
Now, let's substitute the given values:
1/u = 1/15 - 1/20.
To solve this equation, we need to find the common denominator.
15 and 20 have a common multiple of 60.
1/u = (4/60) - (3/60).
1/u = 1/60.
Now, we can solve for u:
u = 60 meters.
Therefore, the distance of the tree from point R is 60 meters.