Test: Mirror Formulae - UPSC MCQ

We know that, if the magnification value is negative sign in the concave mirror, then the image will be real and inverted. Especially, when you come to concave mirror, the images are formed at the left of the mirror. So, it forms real and inverted.

Given: Radius of curvature R = 12 cm
So, focal length f = R / 2 = 6 cm
For concave mirror:
Object distance u = -18 cm (real object in front of mirror)

Using magnification formula: m1 = f / (u - f)
⇒ m1 = 6 / (-18 - 6) = 6 / (-24) = -1/4
For convex mirror:
Object distance u = -18 cm (real object in front)

 

Using magnification formula: m₂ = f / (f - u)
⇒ m₂ = 6 / (6 + 18) = 6 / 24 = 1/4
Now, the ratio of sizes = |m₂| / |m₁| = (1/4) / (1/2) = 1/2
Final Answer: 1/2
Hence, the correct option is (1).

m = ± 3 and f = -6 cm
Now

For real image

For virtual image

CONCEPT:
Concave mirror: 

• If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.
• The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
• The concave mirror can form both real as well as virtual images of any object.

Sign convention in mirrors

• All distance are measured from the pole of the mirror.
• The distance measured from the pole (p) to the left side of the mirror is taken as negative.
• The distance measured from the pole (p) to the right side of the mirror is taken as positive.
• The heights measured upwards and perpendicular to the principal axis of the mirror is taken as positive.
• The heights measured downwards and perpendicular to the principal axis of the mirror is taken as negative.

Explanation:

Given - Radius of curvature (R) = - 30 cm

The relationship between the focal length (f) and the radius of curvature (R) is given by -

- Conclusion: Image is real, inverted, and magnified. Answer C.

CONCEPT:

• Convex mirror: It is an outward curved mirror that produces a diminished image.
  • Convex mirrors either diverge a parallel beam of light into all directions or gather light from all directions and produce a parallel beam out of it.
• Focal length (f): The distance between the centre of the mirror and the focal point (where parallel rays of light meet or appear to meet) of the mirror is called the focal length.
• The radius of curvature (R): The distance between the centre of the lens or mirror to the vertex which is located on the local optical axis is called the Radius of Curvature.
• The focal length is half of the radius of curvature.

f = R/2

CALCULATION:

Given that:
Radius of curvature (R) = 30 cm,
The focal length (f) = R/2 = 30/2 = 15 cm

Object is always kept on the left side of the mirror therefore its distance is always negative when taken from left of pole.

Magnification is thr ratio of size of image to size of object and since it is a ratio of tel similar quantities hence it is unitless. 

Correct option is A.

The image formed by a convex mirror is always smaller in size than the object; hence its magnification is less than 1.