Question

One half of a convex lens of focal length 10 cm is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of 30 cm from the lens? Draw a ray diagram to justify your answer.
A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image.

Answer 1

(i)Yes, it can produce an image of a complete object placed at a distance of 30 cm from the lens.

(ii)Let $h_1$ be the height of the object, f be the focus, u be the distance of the object and v be the distance of the image from lens.
Let $h_2$ be the height of the image formed.
Given: $h_1$ = 4cm , f = + 20cm , u = -15 cm
We know that,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{20}-\frac{1}{15}=\frac{3-4}{60}=\frac{-1}{60}$
$\therefore$ Image distance, v = -60 cm
Image will be virtual and erect.
Now, Magnification , m = $\frac{h_2}{h_1}=\frac{v}{u}$
$h_2=\frac{v}{u}\times h_1=\frac{-60}{-15}\times 4$= +16 cm.
The size of the image is 16 cm.