1.159 Work done in uniform circular motion

Problem 1.159:.A body of mass $‘m’$ is moving in a circle of radius with a constant speed $‘v’$. Calculate the work done by the resultant force in moving the body over half circumference and full circumference respectively. Solution: This is motion along a circular...

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...

5.154 Charge of elementary particles

Problem 5.154:What is the charge of $(i)$ electron $(ii)$ proton and $(iii)$ neutron? Solution: Charge of $(i)$ electron$ = - \:1.6 \times 10^{-19}\:C$                            $(ii)$ Proton$ = + \:1.6 \times 10^{-19}\:C$                            $(iii)$ Neutron=...

6.98 Time taken by light

Problem 6.98:A light ray is incident from air into a glass slab as shown in the diagram. Calculate the time spend by light ray inside glass. Refractive index of glass is $\sqrt{3}$. Solution: Here the ray is making angle of $30^o$ with the plane of the slab. Angle of...

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?...

6.89 Interference of coherent waves

Problem 6.89: Two waves of the same frequency have amplitudes $1.00$ and $2.00$. They interfere at a point where their phase difference is $60^0$.What is the resultant amplitude? Solution: When two waves of amplitude $A$ and $B$ interfere at a point with a phase...

2.101 Buoyant force on a cylinder

Problem 2.101: A cylinder of radius $R$ is kept embedded along the wall of a container of water of density $\rho$. Length of the cylinder is $L$. Determine the vertical force exerted by water on the cylinder. Solution: The cylinder is completely immersed in water. The...

6.88 Image size in a concave mirror

Problem 6.88:A concave mirror forms an image, on a screen $2.00 \:m$ in front of the mirror, of an object $20.0 \:cm$ in front of the mirror. What is the image height if the object height is 5.00 mm? Solution: Here the object  is placed at a distance of $20.0 \:cm$...

6.87 Image formed by a cylindrical glass rod

Problem 6.87: A cylindrical rod made of glass with refractive index $1.5$ is placed in air. It has a hemispherical end surface with radius $2.0\:cm$. A small object is placed at a distance of $6.0\:cm$ on the axis of the rod. Find the location of the image. Solution:...

6.86 Radius of curvature of the mirror

Problem 6.86: A concave mirror forms an image, on a screen $2.00 \:m$ in front of the mirror, of a lamp $20.0 \:cm$ in front of the mirror. Find  the radius of curvature of the mirror? Solution: Here the object, that is the lamp is at a distance of $20.0 \:cm$ and the...

6.85 Image formed by concave mirror

Problem 6.82: A concave spherical mirror has radius of curvature of $20.0 \:cm$. A linear object of height $3.5 \:cm$ is placed $15.0 \:cm$ from the center of the mirror along the optic axis, as shown in the figure.  Calculate the location of the image. Solution:...