Advertisements
Advertisements
Question
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
Solution
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
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 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?
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.
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.
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.
Focal length of a mirror is given by ______.
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.
The intensity of a point source of light, S, placed at a distance d in front of a screen A, is I0 at the center of the screen. Find the light intensity at the center of the screen if a completely reflecting plane mirror M is placed at a distance d behind the source, as shown in the figure.
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 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 ______.
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?
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.
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?
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 ______.
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?
