Question

The origin of x and y coordinates is the pole of a concave mirror of focal length 20 cm. The x- axis is
the optical aixs with x > 0 being the real side of mirror. A point object at the point (25 cm, 1 cm) is
moving with a velocity 10 cm/s in positive x – direction. The velocity of the image in cm/s is
approximately

Answer 1

Answer:

Explanation:

The correct option is C

−

40

^

i

+

2

^

j

Given,

Focal length,

f

=

−

20

cm

Object distance,

u

=

30

cm

Initial height,

h

0

=

1

cm

Velocity of image along positive

x-axis

,

d

u

d

t

=

10

cm/sec

If

v

is the image distance, then

1

v

+

1

u

=

1

f

Substituting the values, we get

1

v

−

1

30

=

−

1

20

⇒

v

=

−

60

cm

For the velocity of image along the

x-axis

we can use,

d

v

d

t

=

−

v

2

u

2

(

d

u

d

t

)

Substituting the values,

v

x

=

−

(

60

30

)

2

×

10

⇒

v

x

=

−

40

cm/sec

Linear magnification

m

=

f

f

−

u

⇒

d

m

d

t

=

−

[

f

(

f

−

u

)

2

]

(

d

u

d

t

)

Substituting the values,

⇒

d

m

d

t

=

−

(

20

)

(

−

20

+

30

)

2

×

10

⇒

d

m

d

t

=

−

2

Velocity of image along

y-axis

v

y

=

d

h

i

d

t

=

−

(

d

m

d

t

)

h

0

⇒

v

y

=

(

−

1

)

×

(

−

2

)

×

1

=

2

cm/s

Negative sign indicates that

h

i

decreases with time.

Velocity of the image

v

I

=

v

x

^

i

+

v

y

^

j

∴

v

I

=

−

40

^

i

+

2

^

j