Question

Two convex thin lenses with focal lengths 10.0 cm and 20.0 cm are aligned on a common axis, running left to right, the 10-cm lens being on the left. A distance of 20.0 cm separates the lenses. An object is located at a distance of 15.0 cm to the left of the 10-cm lens. Where will the final image appear as measured from the 20-cm lens? (a) -13.3 cm (b) -6.67 cm (c) +6.67 cm (d) +13.3 cm (e) +8.1 cm

Answer 1

(c) +6.67

Step-by-step explanation:

f1 = 10 cm

f2 = 20 cm

u = Object distance = 15 cm

Distance between lenses = 20 cm

For first lens image distance

`(1)/(f)=(1)/(u)+(1)/(v)\\\Rightarrow (1)/(f)-(1)/(u)=(1)/(v)\\\Rightarrow (1)/(v)=(1)/(10)-(1)/(15)\\\Rightarrow (1)/(v)=(1)/(30)\\\Rightarrow v=30\ cm`

Distance from second lens is 10 cm to the right

`(1)/(f)=(1)/(u)+(1)/(v)\\\Rightarrow (1)/(f)-(1)/(u)=(1)/(v)\\\Rightarrow (1)/(v)=(1)/(20)-(1)/(-10)\\\Rightarrow (1)/(v)=(3)/(20)\\\Rightarrow v=6.67\ cm`

The final image will appear as +6.67 cm