by Rajan M V | Apr 17, 2016 | Optics

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...
by Rajan M V | Jan 31, 2016 | Optics

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...
by Rajan M V | Jan 17, 2016 | Optics

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...
by Rajan M V | Jan 10, 2016 | Optics

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...
by Rajan M V | Jan 1, 2016 | Optics

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...
by Rajan M V | Dec 15, 2015 | Optics

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...
by Rajan M V | Dec 13, 2015 | Optics

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 $1.5$....
by Rajan M V | Dec 8, 2015 | Optics

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...
by Rajan M V | Dec 6, 2015 | Optics

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?...
by Rajan M V | Oct 6, 2015 | Optics

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...
by Rajan M V | Oct 25, 2014 | Optics

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...
by Rajan M V | Oct 25, 2014 | Optics

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 $H\:=\:40\:m$....
by Rajan M V | Oct 22, 2014 | Optics

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...
by Rajan M V | Oct 21, 2014 | Optics

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...
by Rajan M V | Oct 20, 2014 | Optics

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...
by Rajan M V | Oct 17, 2014 | Optics

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 $4m\:$...
by Rajan M V | Sep 20, 2014 | Optics

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...
by Rajan M V | Aug 9, 2014 | Optics

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...