To determine the nature of the image formed by a concave mirror, we can use the mirror formula given by:
\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
where f is the focal length of the mirror, v is the image distance, and u is the object distance. The focal length (f) is half of the radius of curvature (R), so:
f = \frac{R}{2} = \frac{30\, \text{cm}}{2} = 15\, \text{cm}
Since the object is placed 20 cm in front of the concave mirror, u = -20\, \text{cm} (the negative sign indicates the direction of the object is against the incident light).
Substituting the known values into the mirror formula:
\frac{1}{15} = \frac{1}{v} + \frac{1}{-20}Rearranging gives:
\frac{1}{v} = \frac{1}{15} + \frac{1}{20}To solve for v, find a common denominator and add:
The common denominator of 15 and 20 is 60.
\frac{1}{v} = \frac{4}{60} - \frac{3}{60} = \frac{1}{60}
Thus, v = 60\, \text{cm}.
Since v is positive, the image is formed on the same side as the object, indicating a virtual image.
The magnification (m) is given by:
m = -\frac{v}{u} = -\frac{60}{-20} = 3
The positive magnification value indicates that the image is erect and magnified.
Therefore, the nature of the image formed by the concave mirror in this scenario is magnified, virtual, and erect.
Important Questions from Reflection and Refraction
Human eye can see objects at different distances with contrasting illuminations. This is due to
Light enters the eye through a thin membrane called
The part of the human eye on which the image is formed is
Myopia is a defect in human vision where an image of a
Cornea in human eye
