Understanding Focal Power and Image Formation in Spherical Mirrors

1. Converging or diverging ability of a lens or a mirror is defined as its focal power.
2. This implies that the greater the power of any spherical mirror or lens, the more its ability to converge or diverge the light that passes through it.
3. In the case of a convex lens or concave mirror, the greater the convergence, the shorter the focal length, as shown in the figure.
4. Similarly, in the case of a concave lens or convex mirror, the greater the divergence, the shorter the focal length.
5. This explains that the focal power of any spherical lens or mirror is inversely proportional to the focal length.
6. Hence, the expression for focal power is given by the formula, P = 1f.

Question 4.
At which positions of the objects do spherical mirrors produce (i) diminished image (ii) magnified image?
Answer:
i. Among the two types of spherical mirrors, a convex mirror always produces a diminished image at all positions of the object.

ii. A concave mirror produces a diminished image when the object is placed:

• Beyond the radius of curvature (i.e., u > 2f)
• At infinity (i.e., u = ∞)

iii. A concave mirror produces a magnified image when the object is placed:

• Between the center of curvature and focus (i.e., 2f > u > f)
• Between focus and pole of the mirror (i.e., u < f)

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Question 5.
State the restrictions for having images produced by spherical mirrors to be appreciably clear.
Answer:
i. In order to obtain clear images, the formulae for image formation by mirrors or lenses follow the given assumptions:

• Objects and images are situated close to the principal axis.
• Rays diverging from the objects are confined to a cone of very small angle.
• If there is a parallel beam of rays, it is paraxial, i.e., parallel and close to the principal axis.

ii. In the case of spherical mirrors (excluding small aperture spherical mirrors), rays farther from the principal axis do not remain parallel to the principal axis. Thus, the third assumption is not followed, and the focus gradually shifts towards the pole.

iii. The relation (f = R2) giving a single point focus is not followed, and the image does not converge at a single point, resulting in a distorted or defective image.

iv. This defect arises due to the spherical shape of the reflecting surface.