Advertisements
Advertisements
प्रश्न
A man uses a concave mirror for shaving. He keeps his face at a distance of 25 cm from the mirror and gets an image which is 1.4 times enlarged. Find the focal length of the mirror.
Advertisements
उत्तर
Given,
Distance of the man's face (here, taken as object), u = −25 cm
According to the question, magnification, m = 1.4
\[m = \frac{A'B'}{AB} = - \frac{v}{u}\]
\[ \Rightarrow 1 . 4 = - \frac{(v)}{- 25}\]
\[\Rightarrow\frac{14}{10}=\frac{v}{25}\]
\[\Rightarrow v=\frac{25 \times 14}{10}=35 \text{ cm }\]
Using equation of mirror, we get:
\[\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\]
`⇒ 1/f = 1/35 - 1/25`
\[= \frac{5 - 7}{175} = - \frac{2}{175}\]
⇒ f = −87.5
Hence, the required focal length of the concave mirror is 87.5 cm.
APPEARS IN
संबंधित 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?
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
Following figure shows three transparent media of refractive indices \[\mu_1 , \mu_2 \text{ and } \mu_3\]. A point object O is placed in the medium \[\mu_2\]. If the entire medium on the right of the spherical surface has refractive index \[\mu_3\], the image forms at O". In the situation shown,
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 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?
Consider the situation shown in figure. The elevator is going up with an acceleration of 2.00 m s−2 and the focal length of the mirror is 12.0 cm. All the surfaces are smooth and the pulley is light. The mass-pulley system is released from rest (with respect to the elevator) at t = 0 when the distance of B from the mirror is 42.0 cm. Find the distance between the image of the block B and the mirror at t = 0.200 s. Take g = 10 m s−2.
Two thin lenses having optical powers of -10D and+ 6D are placed in contact with each other. The focal length of the combination is:
According to Cartesian sign convention, all distances are measured from the _______.
The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will ______.
A car is moving with at a constant speed of 60 km h–1 on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h–1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?
An astronomical refractive telescope has an objective of focal length 20 m and an eyepiece of focal length 2 cm.
- The length of the telescope tube is 20.02 m.
- The magnification is 1000.
- The image formed is inverted.
- An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.
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)
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 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 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 ______.
