To solve this problem, we can use the thin lens formula:
1/f = 1/do + 1/di
Where:
f = focal length of the lens
do = object distance (distance between the lens and the slide)
di = image distance (distance between the lens and the screen)
Given:
Height of the image on the screen, hi = 1.5 m
Distance between the projector and the screen, di = 9 m
Height of the picture on the slide, ho = 6.5 cm = 0.065 m
We can use the properties of similar triangles to relate the heights of the object, image, and their distances from the lens:
ho/do = hi/di
Plugging in the given values, we get:
0.065 m/do = 1.5 m/9 m
Solving for do:
do = (0.065 m * 9 m) / 1.5 m
do = 0.39 m
Now, we can use the thin lens formula to find the focal length of the lens:
1/f = 1/do + 1/di
1/f = 1/0.39 + 1/9
1/f = 2.5641 + 0.1111
1/f = 2.6752
f = 1 / 2.6752
f ≈ 0.374 m
Therefore, the distance between the slide (picture) and the lens is approximately 0.39 meters.
the lens of a slide projector focuses an image of height 1.5 m on a screen placed 9 m from the projector. If the height of the picture on the slide is 6.5vm determine the distance between the slide (picture) and the lens
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