Concave Mirror Image Calculation
The question asks for the characteristics of an image formed by a concave mirror, given specific object placement and magnification.
Understanding Magnification and Sign Conventions
- A concave mirror is used.
- The image is real and magnified three times.
- Object distance, u, is 10 cm in front of the mirror. By convention, object distance is negative: u = -10 cm.
- Magnification, m, for a real, magnified image is negative and equals -3.
Calculating Image Distance (v)
The magnification formula for mirrors is:
$ m = -\frac{v}{u} $
Substitute the known values:
$ -3 = -\frac{v}{(-10 \text{ cm})} $
Simplify the equation:
$ -3 = \frac{v}{10 \text{ cm}} $
Solve for v:
$ v = -3 \times 10 \text{ cm} $
$ v = -30 \text{ cm} $
Interpreting the Image Characteristics
- The image distance v = -30 cm. The negative sign indicates the image is formed in front of the mirror.
- The magnification m = -3. The negative sign indicates the image is inverted. The magnitude (3) confirms it is magnified.
- A real image formed by a concave mirror is always inverted.
Therefore, an inverted image is formed at a distance of 30 cm in front of the concave mirror.
Similar Questions
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When an object is kept at a distance 20 cm in front of a concave mirror, a real image is formed at the centre of curvature of the mirroe. Magnification produced by the mirroe is ______________ .
When an object is kept in front of a concave mirror of a focal length of 10 cm, a real image is formed at a distance of 20 cm in front of the mirror. Here, the object distance is .............
Important Questions from Mirrors and Images
- A concave mirror forms a real and inverted image of a distant object at a distance of $15 \text{ cm}$ from the mirror.
If an object is placed $20 \text{ cm}$ in front of this mirror, what will be the nature and magnification of the image formed? The number of images observable between two parallel mirror is
Which of the following pair is correct?
I. Mirror formula : (1/v) – (1/u) = (1/f)
II. Lens formula : (1/v) + (1/u) = (1/f)
- A beam of parallel light, originating from a distant source, is first incident on a convex lens with focal length $f_2$.
Subsequently, the light passes through the lens and then reflects from a concave mirror having a focal length $f_1$.
The concave mirror is placed at a distance $d$ from the convex lens.
For the light rays to retrace their original path and ultimately emerge from the lens as a parallel beam heading back towards the distant source, the separation distance $d$ between the lens and the mirror must be: A ray of light is made incident on a concave mirror, parallel to its principal axis. After reflection it will -
