The power of equi - concave lens is - 4.5 D and is made of a material R.I. 1.6, the radii of the curvature of the lens is
The power of equi - concave lens is - 4.5 D and is made of a material R.I. 1.6, the radii of the curvature of the lens is
- - 2.66 cm
- - 26.6 cm
- 115.44 cm
- +36.6 cm
The Correct Option is B
Solution and Explanation
1/f = (n-1) (1/R1 - 1/R2)
Given:
Power of the lens (P) = -4.5 D
Material refractive index (n) = 1.6
Since the lens is equi-concave, the radii of curvature of both surfaces will have the same magnitude but opposite signs (R1 = - R2)
Using the lens maker's formula and substituting the given values, we can solve for the magnitude of the radii of curvature:
1/f = (1.6 - 1)(1/R - 1/-R)
1/f = 0.6 x 2/R
1/f = 1.2/R
Now, we can find the value of R by rearranging the equation:
R = 1.2/ 1/f
R=1.2⋅f.
Substituting the value of f from the given power, we get:
R = 1.2 x (- 4.5 D-1)
R = - 5.4 m-1
Converting R to centimeters, we have:
R = - 5.4 m-1 . 100 cm/m
R = 540 cm-1
The radii of curvature of the lens is approximately -540 cm or -5.4 m. Among the given options, the closest value to -540 cm is (B) -26.6 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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