Physics 2000 JAMB Past Questions - Question 34: A projection lantern is used to give the image of a slide on a screen. If the image is 24 times as large as the slide and the screen is 72.0m from the projecting lens, what is the position of the slide from the lens?

Correct Answer

C

Explanation

m=v/u ;24 =72/u ;U=3mTo determine the position of the slide from the lens, we can use the concept of similar triangles. The size of the image on the screen is 24 times larger than the slide. This means that the ratio of the size of the image (I) to the size of the slide (S) is 24:To determine the position of the slide from the lens in a projection lantern, we can use the magnification formula:

magnification = image height / object height

In this case, the magnification is given as 24, which means the image is 24 times larger than the slide. Let's assume the object height (slide height) is represented by h, and the image height is 24h.

Since the projection lantern forms an image on the screen, 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, and u is the object distance.

Given that the screen is 72.0m from the projecting lens, we can assume the image distance (v) is 72.0m.

Now, let's solve for the object distance (u):

1/f = 1/v - 1/u

Since the projection lantern is used to give a magnified image, the object distance (u) will be negative. Let's substitute the values into the equation:

1/f = 1/72.0 - 1/u

Since the magnification is given as 24, we can substitute the magnification formula into the equation:

1/f = 1/72.0 - 1/(24h)

Simplifying the equation, we get:

1/f = 1/72.0 - 1/(24 * h)

Now, we can solve for the object distance (u) by rearranging the equation:

1/u = 1/f + 1/v

Substituting the values, we get:

1/u = 1/f + 1/72.0

Simplifying further, we have:

1/u = 1/f + 1/72.0

Now, we can solve for the object distance (u) using the given focal length of the lens.

I / S = 24

Now, let's consider the distance from the lens to the screen (D) and the distance from the lens to the slide (x). Since we have similar triangles, the ratio of these distances must also be 24, because it corresponds to the ratio of the image sizes:

D / x = 24

We are given that the distance from the lens to the screen (D) is 72.0 meters:

D = 72.0 m

Now, we can solve for the distance from the lens to the slide (x):

x = D / 24
x = 72.0 m / 24
x = 3.0 m

So, the position of the slide from the lens is 3.0 meters.