A small candle,2.5cm in size is placed at 27cm in front of a concave mirror of radius of curvature 36cm.At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image.If the is moved closer to the mirror, how would the screen have to be moved?
A small candle,2.5cm in size is placed at 27cm in front of a concave mirror of radius of curvature 36cm.At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image.If the is moved closer to the mirror, how would the screen have to be moved?
Solution and Explanation
Size of the candle,h=2.5cm
Image size=h'
Object distance,u=-27cm
The radius of curvature of the concave mirror, R=-36cm
The focal length of the concave mirror,ƒ=\(\frac{R}{2}\)=-18cm
Image distance=v
The image distance can be obtained using the mirror formula:\(\frac{1}{u}+\frac{1}{v}=\frac{1}{f}\)
\(\frac{1}{v}=\frac{1}{f}-\frac{1}{u}\)=\(\frac{1}{-18}-\frac{1}{-27}\)=\(-3+\frac{2}{54}\)=\(-\frac{1}{54}\)
Therefore, the screen should be placed 54cm away from the mirror to obtain a sharp image. The magnification of the image is given as m=\(\frac{h'}{h}=-\frac{v}{u}\)
∴h'=\(-\frac{v}{u}\)×h=-(\(-\frac{54}{-27}\))×2.5=-5cm
The height of the candle's image is 5cm. The negative sign indicates that the image is inverted and virtual. If the candle is moved closer to the mirror, then the screen will have to move away from the mirror in order to obtain the image.
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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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