Advertisements
Advertisements
प्रश्न
A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take L << |v – f|.
Advertisements
उत्तर
As the mean distance of object from mirror is u
∴ `u_1 = u - L/2` and `u_2 = (u + L/2)`
Let the image of the two ends of object form at distance v1 and v2(v1 > v2). So length of image on principal axis is L' = (v1 – v2)
`1/v + 1/u = 1/f` or `1/v + 1/f = 1/u`
⇒ `1/v = (u - f)/(uf)`
⇒ `v = (uf)/(u - f)`
So L' = `v_1 - v_2 = ((u - L/2)f)/((u - L/2) - f) - ((u + L/2)f)/((u + L/2) - f)`
⇒ L' = `f (u - L/2)/((u - f - L/2)) - (u + 1/2)/((u - f + L/2))`
⇒ L' = `f[((u - L/2)(u - f + L/2) - (u + L/2)(u - f - L/2))/((u - f - L/2)(u - f + 1/2))]`
= `(f[u^2 - uf + (uL)/2 - (uL)/2 + (fL)/2 - L^2/4 - (u^2 - uf - (uL)/2 + (uL)/2 - (fL)/2 - L^2/4)])/((u - f)^2 - L^2/4)`
∴ `L < < (u - f)`
∴ `L^2/4 < < < (u - f)`
So neglecting the terms `L^2/4`
`L^2 = f[((fL)/2 + (fL)/2)/(u - f)^2]`
`L^2 = (ffL)/((u - f)^2` ⇒ `L^2 = (Lf^2)/((u - f)^2`
It is the length of image f.
APPEARS IN
संबंधित प्रश्न
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?
If an object far away from a convex mirror moves towards the mirror, the image also moves. Does it move faster, slower or at the same speed as compared to the object?
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.
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.
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 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?
Two thin lenses having optical powers of -10D and+ 6D are placed in contact with each other. The focal length of the combination is:
With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.
Focal length of a mirror is given by ______.
You are given four sources of light each one providing a light of a single colour – red, blue, green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is 90°. Which of the following statements is correct if the source of yellow light is replaced with that of other lights without changing the angle of incidence?
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?
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 object is 20 cm away from a concave mirror and it is within the focal length of the mirror. If the mirror is changed to a plane mirror, the image moves 15 cm closer to the mirror.
Focal length of the concave mirror is ______.
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.
Why does a car driver use a convex mirror as a rear-view mirror?
