Question

A Bio convex lens of Focal length 15 cm is in Front of a plane mirror the distance between the lens and the mirror is 10cm. A small object is kept at a distance of 30 cm from the Lens. The final image is:
A. Virtual and at a distance of 16 cm from the mirror.
B. Real and at a distance of 16 cm from the mirror.
C. Virtual and at a distance of 20 cm from the mirror.
D. Real and at a distance of 20 cm from the mirror.

Answer 1

Hint:Biconvex lens are simple lenses which consist of two convex surfaces in spherical form, generally having the same kind of curvature.

Complete step by step answer:
We get the image distance by using lens
Formula $${\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}={\displaystyle \frac{1}{f}}\Rightarrow {\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{15}}-{\displaystyle \frac{1}{30}}\Rightarrow v=30\text{ cm}$$
$$v=30\text{ cm}$$ in front of the Convex mirror, which means 20 cm behind the mirror. Assuming a mirror to reflect from both the sides, this image will act as a virtual object for the mirror and second image. $$I_2$$ will be formed at 20 cm in front of the mirror.
1. Understanding the convention used while taking
$$+ve$$ and $$-ve$$sign for Image and object distance, the direction along which ray of light is travel taken as $$+ve$$
2. Focal length:
For convex lens $$+ve$$
For concave lens $$-ve$$

So, here the ray of light is coming from behind the mirror towards lens, for the second image $$I_2$$ with respect to lens,
$$u=+10\text{ cm};f=15\text{ cm}$$
By using lens formula
$${\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}={\displaystyle \frac{1}{f}}$$
$$\Rightarrow {\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{10}}={\displaystyle \frac{1}{15}}$$
$$\Rightarrow v=6\text{ cm}$$
So, this image is at a distance of $$10+6=16\text{ cm}$$ in front of the mirror.

So, the correct answer is “Option B”.

Note:
In this we need to remember that we need to find the distance of the image from the mirror. So we need to add 10 to give a final answer.
Also real images are always inverted in nature. In this converging rays actually made a collection of focus points which we called a real image because generally an image is a collection of focus points in optics.