An object is placed at 15 cm in front of a concave mirror with a focal length of 20 cm. Following the new Cartesian sign convention, the image formed at v = _____.

Question

Question

This question was previously asked in

AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)

Answer 1

The correct answer is +60 cm.

Key Points

The focal length (f) of the concave mirror is -20 cm (negative as per the new Cartesian sign convention).
The object distance (u) is -15 cm (negative as per the new Cartesian sign convention).
The mirror formula is given by 1/f = 1/v + 1/u.
Substituting the given values: 1/(-20) = 1/v + 1/(-15).
Solving the equation, we get v = 60 cm (positive indicating the image is formed on the same side as the object).

Additional Information

Plane Mirrors
- Plane mirrors form virtual images that are the same size as the object.
- The image is laterally inverted and formed behind the mirror at the same distance as the object is in front of it.
Convex Mirrors
- Convex mirrors always form virtual, erect, and diminished images.
- They are used in vehicles' rearview mirrors because they provide a wider field of view.
Lens Formula
- The lens formula is given by 1/f = 1/v - 1/u, which is used for both convex and concave lenses.
- For lenses, the focal length is positive for convex lenses and negative for concave lenses.