(a) Under what conditions is the phenomenon of total internal reflection of light observed ? Obtain the relation between the critical angle of incidence and the refractive index of the medium.
(b) Three lenses of focal lengths +10 cm, –10 cm and +30 cm are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.
Answers
Answer:
(a) Total internal reflection is defined as the phenomenon of reflection of light into a denser medium from an interface of this denser medium and a rarer medium. The conditions for total internal reflection: (i) Incident light ray should travel from a denser medium to a rarer medium. (ii) Angle of incidence, i, should be greater than the critical angle, C, for pair of media in contact. Critical angle is defined as the angle of incidence in denser medium to which angle of refraction is 90° in the rarer medium. Relation between critical angle of incidence and refraction index of the medium: Consider angle of incidence is equal to the critical angle, that is, i = c Then, the angle of refraction is r = 90°. Applying Snell’s law, we have where μd is refractive index of denser medium and μr is refractive index of rarer medium. Therefore, This is the required relation between critical angle of incidence and refractive index of medium.
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Explanation:
focal length of convex lens is, f = +20 cm
Object distance from the lens, u = -60 cm
Distance between the mirror and the lens, d = 15 cm,
Focal length of the mirror, f = +10 cm
Formula: -
The lens formula,
f is the focal length of the lens, v is the image distance, u is the object distance
The mirror formula,
f is the focal length of the mirror, v is the image distance, u is the object distance
Calculations: -
for the lens,
applying the lens formula,
After solving we get,
v’ = +30 cm
This image is the object for the mirror, which is formed at 15 cm behind the mirror, so this is the case of a virtual object
Applying the mirror formula, we get,
After solving we get,
v = +30 cm
So, the final image is formed 30 cm behind the mirror is virtual in nature.