Advertisements
Advertisements
प्रश्न
Answer the following question.
Three lenses of focal length +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.
Advertisements
उत्तर
`1/v - 1/u = 1/f`
`u = -30 cm`
`f = +10 cm`
`1/nu = 1/f + 1/u`
`1/nu_1 = 1/10 - 1/30`
⇒ `1/nu_1 = (3 - 1)/30 = 2/30`
`nu_1 = 15` cm
`u = +10 cm`
`f = -10 cm`
`1/nu_2 = 1/f + 1/u = 1/10 - 1/10`
`nu_2 = ∞`
For third lens object is at infinity hence image is formed at focus final image at a distance of 30 cm.
संबंधित प्रश्न
A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.
A converging lens of focal length 12 cm and a diverging mirror of focal length 7.5 cm are placed 5.0 cm apart with their principal axes coinciding. Where should an object be placed so that its image falls on itself?
A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 40 cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?
A converging lens of focal length 40 cm is kept in contact with a diverging lens of focal length 30 cm. Find the focal length of the combination .
How can the spherical aberration produced by a lens be minimized?
A thin convex lens of focal length 25 cm is cut into two pieces 0.5 cm above the principal axis. The top part is placed at (0, 0) and an object placed at (– 50 cm, 0). Find the coordinates of the image.
(i) Consider a thin lens placed between a source (S) and an observer (O) (Figure). Let the thickness of the lens vary as `w(b) = w_0 - b^2/α`, where b is the verticle distance from the pole. `w_0` is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(ii) A gravitational lens may be assumed to have a varying width of the form
`w(b) = k_1ln(k_2/b) b_("min") < b < b_("max")`
= `k_1ln (K_2/b_("min")) b < b_("min")`
Show that an observer will see an image of a point object as a ring about the center of the lens with an angular radius
`β = sqrt((n - 1)k_1 u/v)/(u + v)`
A spherical mirror is obtained as shown in the figure from a hollow glass sphere. if an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)
A concave mirror of focal length 12 cm forms three times the magnified virtual image of an object. Find the distance of the object from the mirror.
A lens of focal length f is divided into two equal parts and then these parts are put in a combination as shown in the figure below.
- What is the focal length of L1?
- What is the focal length of the final combination?
