A personneedsa lensof power-5.5dioptres forcorrectinghisdistantvision.Forcorrectinghis nearvision,he needsa lensof power+ 1.5dioptres. What is thefocallengthof therequiredforcorrecting(i)distant vision, and (ii)nearvision ?

A personneedsa lensof power-5.5dioptres forcorrectinghisdistantvision.

1.	A personneedsa lensof power-5.5dioptres forcorrectinghisdistantvision.Forcorrectinghis nearvision,he needsa lensof power+ 1.5dioptres. What is thefocallengthof therequiredforcorrecting(i)distant vision, and (ii)nearvision ?
Answer» Solution :(i)fordistant VISION: Powerof LENS ,P=-5.5D Now ,Power , `P=(1)/(f"(in metres)")""("where f=Focal length ")` SO, `-5.5=(1)/(f)` And , `f=(1)/(-5.5)m` Or , `f=-(1)/(5.5)xx100cm` So, Focal length f=-18.18 CM `""`(or-18.2cm) thusthe focal lengthof lens requiredforcorrecingdistant visionis, - 18.2 cm. Minus signof focallengthtells us that it is a concave lens. (ii)fornearvision: power of lens, P=+ 1.5D Now, Power, `P=(1)/(f"(metres)") ` So `+1.5 =(1)/(f)` And `f=(1)/(+1.5)m` Or, `f = +(1)/(1.5)xx100cm` So,focal length, f = + 66.66 cm(or + 66.7 cm) Thusthe FOCALLENGTH of lensrequiredforrequiredfor correctingnearvisionis +66.7 cmPlussign of focallength tellsus thatit isa convex lens.