A convex lens forms a real and inverted image of a pencil at a distance of 40 cm from the lens. The image formed is of the same size as the object Find the focal length and power of the lens. At what distance is the : object placed from the lens?

A convex lens forms a real and inverted image of a pencil at a distanc

1.	A convex lens forms a real and inverted image of a pencil at a distance of 40 cm from the lens. The image formed is of the same size as the object Find the focal length and power of the lens. At what distance is the : object placed from the lens?
Answer» <P> Solution :Step 3: Use formula `M=(v)/(u)=(h_(2))/(h_(1))"……(i)"` We are given that, `h_(2)=-h_(1)` Substituting for `h_(2)` in equation (i), `M=(-h_(1))/(h_(1))=-1` `therefore" "-1=(v)/(u)=(40)/(u)` `therefore" "u=-40 cm` (-ve sign indicates OBJECT is placed at left of lens) Step 4: Now, to calculate focal length, use formula `(1)/(f)=(1)/(v)-(1)/(v)"....(ii)"` Substituting values for object distance (u-40 cm) and image distance (v= + 40 cm), `(1)/(f)=(1)/(40)-(1)/(-40)+(1)/(40)=(2)/(40)=(1)/(20)` `therefore" "f=20 cm` Focal length of a lens `=20 cm =0.2 m` Step 5: Formula for calculating POWER of lens is given as, `P=(1)/(f)` Keep in mind that the above formula for power of lens is VALID only when the focal length of the lens is measured in metre. `therefore" "P=(1)/(0.2)=5D`