An object of size 3.0 cm is placed 14cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?
An object of size 3.0 cm is placed 14cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?
Solution and Explanation
Size of the object,h1=3cm
Object distance,u=-14cm
Focal length of the concave lens,f=-21cm
Image distance=v
According to the lens formula, we have the relation:
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)
=\(\frac{1}{v}=-\frac{1}{21}-\frac{1}{14}\)
=-2\(-\frac{3}{42}\)=\(-\frac{5}{42}\) ∴v=\(-\frac{42}{5}\)=-8.4cm
Hence,the image is formed on the other side of the lens,8.4cm away from it. The negative sign shows that the image is erect and virtual.The magnification of the image is given as:m=Image height(h2)/Object height(h1)=\(\frac{v}{u}\) ∴h2=\(\frac{-8.4}{-14}\)×3=0.6×3=1.8cm
Hence, the height of the image is 1.8cm.If the object is moved further away from the lens, then the virtual image will move toward the focus focus of the lens, but not beyond it. The size of the image will decrease with the increase in the object distance.
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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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