Advertisements
Advertisements
Question
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?
Options
The speed of the car in the rear is 65 km h–1.
In the side mirror the car in the rear would appear to approach with a speed of 5 km h–1 to the driver of the leading car.
In the rear view mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.
In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
Advertisements
Solution
In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
Explanation:
Object moving along the principal axis: On differentiating the mirror formula with respect to time, we get `(dv)/(dt) = - (v/u)^2 (du)/(dt) = - (f/(u - f))^2. (du)/(dt)`. where `(dv)/(dt)` is the velocity of image along the principal axis and `(du)/(dt)` is the velocity of object along the principal axis. A negative sign implies that the image, in case of mirror, always moves in the direction opposite to that of the object.
As the distance between the cars decreases, the speed of the image of the car would appear to increase.
APPEARS IN
RELATED QUESTIONS
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.
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?
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,
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?
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 .
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.
According to the mirror equation, ______.
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?
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|.
(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)`
Why does a car driver use a convex mirror as a rear-view mirror?
