A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is:
A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is:
−15 cm
45 cm
−45 cm
15 cm
The Correct Option is A
Solution and Explanation
Step 1: Given Parameters
Radius of curvature \(R = 30 \, \text{cm}\). For a mirror, focal length \(f = \frac{R}{2} = +15 \, \text{cm}\) (positive for a convex mirror).
Step 2: Use the Magnification Formula for Mirrors
Given that the image is half the size of the object, the magnification \(m = \frac{1}{2}\). For a convex mirror, a virtual image is formed for a real object, so \(m\) is positive:
\[ m = +\frac{1}{2} \]
Step 3: Apply the Mirror Formula
The magnification formula is \(m = \frac{f}{f - u}\). Substitute \(m = \frac{1}{2}\) and \(f = 15 \, \text{cm}\):
\[ \frac{1}{2} = \frac{15}{15 - u} \]
Step 4: Solve for \(u\)
\[ 15 - u = 30 \implies u = -15 \, \text{cm} \]
So, the correct answer is: -15 cm
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Concepts Used:
Ray Optics and Optical Instruments
Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.
Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.
Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.
Speed of light is the rate at which the light travels in free space.
A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.
Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.
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