Aspherical mirror produces an image of magnification-1 on a screen placed at a distance of 50 cm from the m
Witte the type of the mirror.
What is the focal length of the mirror?
(i) Find the distance of the image for the object. (iv) Draw the ray diagram to show the image formation in tha?

Question

Answer

Solution:

Given data:
- Magnification (m) = -1
- Distance of the screen (v) = 50 cm

Focal length of the mirror:
- Since the magnification is -1, the mirror must be a concave mirror.

(i) Distance of the image for the object:
- Magnification (m) = -v/u, where u is the distance of the object from the mirror.
- Given m = -1, v = 50 cm, solving for u, we get: u = -50 cm
- The distance of the object from the mirror is -50 cm.

(ii) Focal length of the mirror:
- Using the mirror formula: 1/f = 1/v + 1/u
- Given v = 50 cm, u = -50 cm, solving for f, we get: f = -25 cm
- The focal length of the mirror is -25 cm.

Ray diagram:
- Draw the concave mirror with the focal point F and the center of curvature C.
- Place the object between F and the mirror, at a distance of 50 cm.
- Draw two rays: one parallel to the principal axis that passes through F after reflection, and one that passes through C and reflects back along itself.
- The point where the two rays intersect after reflection will be the image of the object.
- The image will be real, inverted, and of the same size as the object.
This is how the image formation takes place in a concave mirror with a magnification of -1.

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