Optimizing Lens Combination for Smallest Image Projection

How can we determine the point and height of the smallest image projected on the screen?

a) At what point between the object and the screen will the smallest image be projected on the screen?

b) If the object is 5 cm tall, how tall is the smallest image on the screen?

Answer:

The smallest image is projected at a point 60 cm from the object. If the object is 5 cm tall, the height of the smallest image on the screen can be determined using the magnification formula.

To find the point between the object and the screen where the smallest image will be projected, we need to 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.

Using the lens formula for each lens with focal lengths of 15 cm and 20 cm, we can find the image distances. By calculating the combined focal length of the two lenses, it can be found that the smallest image is formed at a distance of 60 cm from the object.

To determine the height of the smallest image, we can use the magnification formula: m = -v/u. Given that the object is 5 cm tall, we can calculate the magnification produced by the lenses and then multiply it by the object's height. The resulting height of the smallest image on the screen can be obtained through this calculation.

Final answer: To find the point between the object and the screen where the smallest image will be projected, use the lens formula and compare the magnifications of each lens. The height of the smallest image can be determined using the magnification formula.