Answer to Question #103761 in Optics for Tanish George Mathew

Question

if an object is placed at 40 cm and its image is formed at 2 times focal length, where the image is inverted? then name the types of lens and find where the image is formed.

Answer 1

Solution. Using the lens formula

$$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$$

where f is focal lenth; u is object distance; v is image distance.

According to the condition of the problem, the u= 40 cm=0.4m, v=2f. Therefore

$$\frac {1} {u} =\frac{1}{f} -\frac{1}{2f}$$

$$u=2f=0.4m$$

Therefore, the focal length of the lens is equal to 20 cm =0.2m and v=0.4m.

The actual image when placing the object in the double focus of the lens gives a convex lens.

Ray diagram for this case (a diagram can be obtained by constructing an image of an object based on the position the image)

Answer. convex lens, v=0.4m.