(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.
(b) Let us consider the given lenses to be denoted as 1, 2, and 3, respectively, as shown in the following figure:
Given:
• Focal length of lens 1 = +10 cm
• Focal length of lens 2 = –10 cm
• Focal length of lens 3 = +30 cm
Applying lens formula, we get
For lens 1, we have f = +10, v = x, and u = –30 cm. Therefore,
Thus, for lens 2, the image of lens 1 at distance x = 15 cm is the object. Therefore,
f = - 10 cm
v = x
u = 15 cm - 50 cm = 10 cm
Therefore,
Thus, for lens 3, image of lens 2 is the object, which is located at infinity.
We know that for a convex lens, rays coming from infinity converge at the focus. Thus, image is formed at the focus of lens 3, that is, at 30 cm.
Thus, the final image formed by the combination is at 30 cm.
