(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.

(a) A security mirror used in a big showroom has radius of curvature 5

1.	(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.
Answer» Solution :The security mirror is a convex mirror whose radius of curvature R = +5 m or FOCAL length `f=(R )/(2)= +2.5m`, distance of object (customer) from the cash counter (i.e., the image) u = 20m and as per sign convention u is -ve i.e., u = -20 m. As per mirror formula `(1)/(v)+(1)/(u)=(1)/(f)`, we have `(1)/(v)=(1)/(f)-(1)/(u)=(1)/((+5))-(1)/((-20))=(1)/(5)+(1)/(20)=(1)/(4)` `RARR v=4 m and m=(-v)/(u)=(-4)/((-20))=+0.2` Thus, image is formed at a distance of 4 m BEHIND the security mirror. The image is virtual, erect and diminished one (of magnification 0.2). (B) The mirror used by dentist is a concave mirror. Dentist used this mirror so as to form large images of the teeth of patients so that he can examine them easily and in more details.