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

Focal length of the convex lens is 20 cm and its power is 5 D. The object is placed at a distance 40 cm.

Explanation

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`