An object `5 cm` in length is held `25 cm` away from a converging lens of focal length `10 cm`. Draw the ray diagram and find the position, size and the nature of the image formed.

Explanation

A vonverging lens means a vonvex lens. Now, first of all we will find the position of image by calculating the image distance v.
Here, Object distance, u = -25 cm (It is to the left of lens)
Image distance, v = ? (To be calculated)
And, Focal length, f = + 10 cm (It is a converging lens or convex lens )
Now, putting these values in the lens formula :
`1/v-1/u=1/f`
`"We get: "1/v-1/(-25)=1/10`
`/v+1/25=1/10`
`1/v=1/10-1/25`
`1/v=(5-2)/50`
`1/v=3/50`
`v=+50/3`
v=+16.67 cm
Thus, the position of image is at ata distance of 16.67 cm form the lens. The plus sign for image distance shows that the image is formed on the right side of lens (or behind the lens) and that nature of image is real and inverted.
Let us calcualte the magnification now. For a lens :
`"Megnification, "m=v/u`
`m=(16.67)/(-25)`
m = -0.66
We will now calculate the size of image `h_(2)`
by knowing the size of object `h_(1)` and value of m.
`"Now, "m=h_(2)/h_(1)`
`"So, "-0.66=h_(2)/5`
`h_(2)=-0.66xx5`
`h_(2)= - 3.3 cm`
Thus, the size of image is 3.3 cm. The nagative sign of the size of image shows that the image is inverted.