(a) A security mirror used in a big showroom has radius of curvature 5 m. If a customer is standing at a distance of 20 m from the cash counter, find the position, nature and size of the image formed in the security mirror.

(b) Neha visited a dentist in his clinic. She observed that the dentist was holding an instrument fitted with a mirror. State the nature of this mirror and reason for its use in the instrument used by dentist.

OR

Rishi went to a palmist to show his palm. The palmist used a special lens for this purpose.

(i) State the nature of the lens and reason for its use.

(ii) Where should the palmist place/hold the lens so as to have a real and magnified image of an object?

(iii) If the focal length of this lens is 10 cm and the lens is held at a distance of 5 cm from the palm, use lens formula to find the position and size of the image.

Part (a)

• Position of the image: $2.22\text{ m}$ behind the mirror.
• Nature of the image: Virtual and erect.
• Size of the image: Highly diminished (size is $\frac{1}{9}$ of the object's size).

Part (b)

• Nature of the mirror: Concave mirror.
• Reason for use: When held close to the teeth, the teeth lie within its focal length (between the pole and focus), producing an erect, virtual, and highly magnified image of the teeth, allowing the dentist to see details clearly.

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OR

Part (i)

• Nature of the lens: Convex lens (Converging lens).
• Reason for use: It forms an erect, virtual, and magnified image of the fine lines of the palm when held close to it (within its focal length).

Part (ii)

• Position: The palmist should place/hold the lens such that the palm (object) is located between the principal focus ($F$) and twice the focal length ($2F$) of the lens.

Part (iii)

• Position of the image: $10\text{ cm}$ in front of the lens (on the same side as the palm).
• Size of the image: Twice the size of the object (magnified by a factor of $2$).