Advertisements
Advertisements
Question
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.
Advertisements
Solution
If a symmetric lens is cut parallel to principal axis in two parts. The focal length remains the same for each part. The intensity of image formed by each part will be less compared to that of the complete lens.
If there was no cut, then the object would been at a height of 0.5 cm from the principal axis O'.
The top part is placed at (0, 0) and an object is placed at (– 50 cm, 0). There is no effect on the focal length of the lens.
u = – 50 cm, f = 25 cm, v = ?
`1/v - 1/u = 1/f`
`1/v - 1/(-50) = 1/25`
`1/v = 1/25 - 1/50`
= `(2 - 1)/50 = 1/50`
v = 50 cm
`m = (+v)/u = (+(50))/(-50)` = – 1
So the size of image is equal to that of object, m is negative so image is inverted.
So image is at (50 cm), – 1 cm) and 0.5 cm below the X – x' axis.
APPEARS IN
RELATED QUESTIONS
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 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
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?
Can mirrors give rise to chromatic aberration?
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 U-shaped wire is placed before a concave mirror having radius of curvature 20 cm as shown in figure. Find the total length of the image.
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.
The image of an extended object, placed perpendicular to the principal axis of a mirror, will be erect if
(a) the object and the image are both real
(b) the object and the image are both virtual
(c) the object is real but the image is virtual
(d) the object is virtual but the image is real.
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 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 .
Two thin lenses having optical powers of -10D and+ 6D are placed in contact with each other. The focal length of the combination is:
Answer the following question.
Under what conditions is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.
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.
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 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.
