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A concave mirror (R = 56.7 cm) is used to project a transparent slide onto a wall. The slide is located at a distance of 36.3 cm from the mirror, and a small flashlight shines light through the slide and onto the mirror.

(a) How far from the wall should the mirror be located?

(b) The height of the object on the slide is 1.55 cm. What is the height of the image?

Answer :

Final answer:

Using optics formulas for concave mirrors, it's possible to find the distance from the mirror to the wall and the height of the image from the given values. The mirror formula and magnification formula are key to solve this problem.

Explanation:

To answer this question, we need to use the mirror formula and magnification formula from optics. The mirror formula is 1/f = 1/v + 1/u and the magnification formula is m = -v/u. Here, f represents the focal length, v is the image distance, u is the object distance, and m represents the magnification. Remember, the radius of curvature R is twice the focal length f for a mirror, i.e., R = 2f.

(a) Given that the radius of curvature R = 56.7 cm, the focal length f is half of R, i.e., 28.35 cm. Plugging the values into the mirror equation where the object distance u = -36.3 cm (negative because the object is on the same side as the light source), we can solve for v, the image distance. This gives us the distance from the mirror to the wall.

(b) To find the height of the image, we use the magnification equation. Given that the height of the object is 1.55 cm, we find the height of the image by multiplying the object height by the magnification.

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