What is the nature of the image formed by a convex lens if the magnification produced by the length is 3?

1. Laws of Reflection of Light:

(i) Angle of incidence is equal to angle of reflection

(ii) Incident ray, reflected ray, normal drawn to the reflecting surface at the point of incidence, lie in a same plane.

2. Laws of Refraction of Light:

(i) For a given pair of medium, and for given colour of light, the ratio between the sine of angle of incidence and sine of angle of refraction is constant and equal to relative refractive index of medium 2 with respect to medium 1.

If i is the angle of incidence and r is the angle of refraction, then sin isin r= constant.

(ii) Incident ray, refracted ray, normal drawn to the interface, at the point of incidence, lie in a same plane.

3. Spherical Mirrors:

(i) A mirror, which is polished from the outer side of a hollow sphere, such that the reflecting side is towards hollow side, is called a concave mirror.

(ii) A mirror which is polished from the hollow side of the sphere, such that the reflecting surface is towards bulging side, is called a convex mirror.

(iii) The focal length f of a spherical mirror is half of the radius of curvature R. f=R2

(iv) The mirror formula for spherical mirrors is 1v+1u=1f and gives the relationship between object distance u, image distance v and the focal length f.

(v) The magnification produced by a spherical mirror, m=-vu.

4. New Cartesian Sign Conventions:

In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis of the coordinate system. The conventions are as follows –

(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

(ii) All distances parallel to the principal axis are measured from the pole of the mirror.

(iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along - x-axis) are taken as negative.

(iv) Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

(v) Distances measured perpendicular to and below the principal axis (along - y-axis) are taken as negative.

5. Refraction of Light:

(i) The phenomenon due to which a ray of light deviates from its path at the

of the separation of two media, when the ray of light is travelling from one optical medium to another optical medium is called refraction of light.

(ii) The rays of light while travelling from rarer to denser medium bend towards the normal drawn at the point of incidence. The rays travelling from a denser to a rarer medium, bend away from the normal.

(iii) Refractive index of a medium, μ=Speed of light in vacuumSpeed of light in the medium.

(iv) Relative refractive index of medium 2 with respect to medium 1, μ2,1=Speed of light in medium 1Speed of light in medium 2.

(v) In a rectangular glass slab, when light is passing through two opposite faces, angle of incidence is always equal to that angle of the emergence.

6. Refraction by Spherical Lenses:

(i) Lens formula for spherical lens is 1v-1u=1f and gives relationship between object distance u, image distance v and the focal length f.

(ii) Magnification produced by a lens, m=vu.

(iii) Power of lens P is the reciprocal of its focal length f in metre. The SI unit of power of a lens is dioptre (D). P=1fin metre.

Option 3 : m = -1/2 real and inverted image

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The correct answer is option 3, i.e., m = -1/2 real and inverted image.

The magnification and nature of the image formed by the convex lens are: m = 1/2 real and inverted image.
The formula of magnification produced by a spherical lens is: m = v / u ⇒ m = height of the image/ height of the object
We are given the focal length and the image distance, so we can calculate the object distance by using the following formula and method:
- 1/f = 1/v - 1/u
- 1/20 = 1/30 - 1/u (focal length and image distance are positive)
- 1/u = 1/30 - 1/20
- 1/u = -1/60
- u = -60 cm
Now, we can calculate magnification by substituting the value of 'u' into its formula:
- m = v / u
- m = 30 / -60
- m = -1/2
The magnitude of the magnification shows that image is diminished, while its -ve sign shows that the image is real and inverted.