Question

What are the laws of refraction? An object of 3 cm is placed perpendicular to the principal axis of a convex lens. Focal length of the lens is 30 cm and the distance of the object from lens is 10 cm. Find the position, size, and nature of the image. Can we observe this image on a screen?

Hint:

For virtual images formed by convex lenses, the image cannot be projected onto a screen as it is formed on the same side as the object.

Answer 1

Laws of Refraction:
Refraction is the bending of light as it passes from one medium to another. The laws of refraction are:
1.
First law:
The incident ray, the refracted ray, and the normal to the surface of the interface of the two media all lie in the same plane.
2.
Second law:
The ratio of the sine of the angle of incidence (\( i \)) to the sine of the angle of refraction (\( r \)) is constant and is known as the refractive index (\( n \)) of the medium:
\[ \frac{\sin i}{\sin r} = n \] This is known as Snell's law.

Given:
- Focal length of the convex lens, \( f = 30 \, \text{cm} \)
- Object distance, \( u = -10 \, \text{cm} \) (since the object is on the same side as the incoming light)
- Object height, \( h_o = 3 \, \text{cm} \)

Using the lens formula:
The lens formula relates the object distance (\( u \)), image distance (\( v \)), and focal length (\( f \)) of a lens:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Substituting the given values:
\[ \frac{1}{30} = \frac{1}{v} - \frac{1}{(-10)} \] \[ \frac{1}{v} = \frac{1}{30} - \frac{1}{10} = \frac{1 - 3}{30} = \frac{-2}{30} \] \[ v = -15 \, \text{cm} \]
Position of the Image:
The image is formed at \( v = -15 \, \text{cm} \), which means the image is formed on the same side as the object. Since the image distance is negative, it is a virtual image.

Size of the Image:
The magnification (\( M \)) of the lens is given by:
\[ M = \frac{h_i}{h_o} = \frac{v}{u} \] Substituting the known values:
\[ M = \frac{-15}{-10} = 1.5 \] Thus, the image height \( h_i \) is:
\[ h_i = M \times h_o = 1.5 \times 3 = 4.5 \, \text{cm} \]
Nature of the Image:
The image is virtual, erect, and magnified because it is formed on the same side as the object.

Can we observe the Image on a Screen?
Since the image is virtual and formed on the same side as the object, it cannot be observed on a screen. It can only be seen by looking through the lens.

Conclusion:
The image formed is virtual, erect, and magnified. It is formed at a distance of \( 15 \, \text{cm} \) from the lens and has a height of \( 4.5 \, \text{cm} \). This image cannot be observed on a screen.