Advertisements
Advertisements
प्रश्न
A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
उत्तर
Size of the candle, h = 2.5 cm
Image size = h'
Object distance, u = −27 cm
Radius of curvature of the concave mirror, R = −36 cm
Focal length of the concave mirror, f = `"R"/2 = (-36)/2` = −18 cm
Image distance = v
The image distance can be obtained using the mirror formula:
`1/"u" + 1/"v" = 1/"f"`
`1/"v" = 1/"f" - 1/"u"`
= `1/-18 - 1/-27`
= `(-3 + 2)/54`
= `-1/54`
∴ v = −54 cm
Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image.
The magnification of the image is given as:
`"m" = "h'"/"h" = - "v"/"u"`
∴ h' = `-"v"/"u" xx "h"`
= `-(-54)/(-27) xx 2.5`
= −5 cm
The height of the candle’s image is 5 cm. The negative sign indicates that the image is inverted and real.
If the candle is moved closer to the mirror, then the screen will have to be moved away from the mirror in order to obtain the image.
APPEARS IN
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.
In motor vehicles, a convex mirror is attached near the driver's seat to give him the view of the traffic behind. What is the special function of this convex mirror which a plane mirror can not do?
In image formation from spherical mirrors, only paraxial rays are considered because they
Light is incident from glass (μ = 1.5) to air. Sketch the variation of the angle of deviation δ with the angle of incident i for 0 < i < 90°.
A spherical surface of radius 30 cm separates two transparent media A and B with refractive indices 1.33 and 1.48 respectively. The medium A is on the convex side of the surface. Where should a point object be placed in medium A so that the paraxial rays become parallel after refraction at the surface?
A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius r. What should be the refractive index is the pencil is to be focussed (a) at the surface of the sphere, (b) at the centre of the sphere.
A diverging lens of focal length 20 cm and a converging mirror of focal length 10 cm are placed coaxially at a separation of 5 cm. Where should an object be placed so that a real image is formed at the object 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?
According to Cartesian sign convention, all distances are measured from the _______.
A thin converging lens of focal length 12 cm is kept in contact with a thin diverging lens of focal length 18 cm. Calculate the effective/equivalent focal length of the combination.
A parallel beam of light ray parallel to the x-axis is incident on a parabolic reflecting surface x = 2by2 as shown in the figure. After reflecting it passes through focal point F. What is the focal length of the reflecting surface?
The direction of ray of light incident on a concave mirror is shown by PQ while directions in which the ray would travel after reflection is shown by four rays marked 1, 2, 3 and 4 (figure). Which of the four rays correctly shows the direction of reflected ray?
(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)`
Parallel rays striking a spherical mirror far from the optic axis are focussed at a different point than are rays near the axis thereby the focus moves toward the mirror as the parallel rays move toward the outer edge of the mirror. What value of incidence angle θ produces a 2% change in the location of the focus, compared to the location for θ very close to zero?
A particle is dropped along the axis from a height 15 cm on a concave mirror of focal length 30 cm as shown in figure. The acceleration due to gravity is 10 m/s2. Find the maximum speed of image in m/s:
A converging lens has a focal length of 10 cm in air. It is made of a material with a refractive index of 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length.
If an object is placed at a distance of 10 cm in front of a concave mirror of a focal length of 20 cm, the image formed will be ______.
Why does a car driver use a convex mirror as a rear-view 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?
