6.99 Effective focal length

6.99: A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surface are of the same radius of curvature $R \:=\: 14\:cm$. Find the...

6.97 Law of reflection.

Problem 6.97:A ray of light initially travelling horizontally,  is incident on the reflecting surface of a hemispherical object and gets deflected vertically upward as shown in the diagram. Find the value of height, $H$ at which the ray hit the object. Solution: The...

6.96 Angle of incidence

Problem 6.96: A ray is incident on a transparent  slab of refractive index $\sqrt{3}$.   The reflected and the refracted rays are mutually perpendicular.  Find the  angle of incidence. Solution: With reference to the diagram, $AO$ is the incident ray that makes angle...

6.95 Refractive index of a medium

Problem 6.95:Speed of light in a medium is one-third of the speed of light in vacuum. Determine the refractive index of the medium Solution: By definition refractive index $(n)$ of a medium is the ratio of speed of light in vacuum $(c)$to speed of light in that medium...

6.94 Angle of deviation in refraction

Problem 6.94: A plane separates a transparent media of refractive index of $\sqrt{3}$ from air. A ray of light coming from air is incident at an angle of $60^o$. Determine the angle of deviation of the ray. Solution: The light ray gets refracted as it enters the...

6.93 Focal length of a convex lens

Problem 6.93: A lens is made of glass having an index of refraction of $1.5$. Sides  of the lens are convex with a radius of curvature of $20 \:cm$. $(a)$ Find the focal length of the lens.  Solution: For a thin lens we have the relation...

6.92 Refraction at spherical surface

Problem 6.92: A point sized  object is buried in a spherical glass pebble of diameter $6.0\:cm$. The object appears at a depth of $2.0\:cm$ when viewed normal to the surface of the pebble. Find out how deep it actually is. Glass has refractive index of $1.5$....

6.91 Minimum intensity in diffraction

Problem 6.91: What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at $\theta\:=\: 45.0^0$ ? Solution: In diffraction $n^th$ order minima is obtained at an angle given by...

6.90 Fringe width in interference

Problem 6.90: In Young’s double slit experiment two narrow slits $0.8\:mm$ apart are illuminated by the same source of yellow light of wavelength $600\:nm$. How far apart are the adjacent bright bands in the interference pattern observed on a screen $2\:m$ away?...

6.80 Focal length of a concave mirror

Problem 6.80:Determine the focal length of a concave mirror of radius of curvature $40\:cm$ in air and in water. Refractive index of water is approximately $\frac{4}{3}$. Solution: Focal length  a mirror of radius of curvature $R$  in air is...

6.79 Interference of light

Problem 6.79: Two interfering beams has intensities in the ratio $9:4$.  Find the ratio of maximum amplitude to minimum amplitude in the interference pattern. Solution: If $I_1$ and $I_2$ are the intensities of interfering waves then the maximum intensity in the...

6.78 Apparent depth

Problem 6.78: A tank of height $40\:m$ is filled with oil fully.   When viewed from vertically above the surface, the bottom of the tank appears to be $30\:m$ below its top. What is the refractive index of the oil ? Solution: The real depth of oil is $H\:=\:40\:m$....

6.77 Focal length of a planoconvex lens

Problem 6.77: The radius of curvature of a thin convex surface of a planoconvex lens is $10\:cm$ and the focal length of the lens is $30\:cm$. Find the refractive index of the material of the lens. Solution: Let light fall on the flat surface and refract through the...

6.76 Angular magnification of telescope

Problem 6.76: A small telescope has an objective lens of focal length $140\:cm$ and an eyepiece of focal length $5.0\:cm$. What is the magnifying power of the telescope for viewing distant objects when the telescope is in normal adjustment $($ i.e., when the final...

6.75 Refraction in prism

Problem 6.75: A ray of light is incident at an angle of $60^o$ on one face of prism of angle $30^o$.  The emergent ray of light makes an angle of $30^o$ with incident ray.  Find the angle made by emergent ray with second face of prism. Solution:   For a...

6.74 Angular size of image formed by a telescope

Problem 6.74: The diameter of the moon is $3.5 \times 10^3\: km$ and its distance from the earth is $3.8 \times 10^5\: km$.  Seen, Calculate the diameter of the image  of the moon formed by a telescope having focal lengths of the objective and the eye-piece as $4m\:$...

6.73 Fresnel distance

Problem 6.73: Light of wavelength $6000\:A^o$ is incident on a circular hole of diameter $2\:mm$. Determine the distance from the hole beyond which the spreading of light becomes significant. Solution: When light passes through a tiny hole, it spreads out. This is...

6.72 Focal length of the lens

Problem 6.72: A lens is made of glass having an index of refraction of $1.5$. One side of the lens is flat, and the other is convex with a radius of curvature of 20 cm. Find the focal length of the lens. Solution:   Let light fall on the flat surface and refract...