Question

The spherical side mirror on a car is convex and has a radius of curvature of 25 cm. Another car is following, 20 m behind the mirror. If the height of the car is 1.6 m, how tall is its image? (A) 5.0 cm (B) 2.0 cm (C) 4.0 cm (D) 0.99 cm

Answer 1

The height of the image formed by the convex side mirror is approximately 0.944 cm.

Step-by-step explanation:

To find the height of the image formed by the convex side mirror, we can use the mirror equation:

1/v + 1/u = 1/f

where v is the image distance, u is the object distance, and f is the focal length.

Given:

• Radius of curvature (R) = 25 cm (since the mirror is convex)
• Distance of the car from the mirror (u) = 20 m = 2000 cm
• Height of the car (h) = 1.6 m = 160 cm

The focal length (f) can be calculated using the formula: f = R/2

So, f = 25 cm / 2 = 12.5 cm

Now, substitute the values into the mirror equation and solve for v:

1/v + 1/u = 1/f

1/v + 1/2000 = 1/12.5

1/v = 1/12.5 - 1/2000

1/v = (160 - 12.5) / (12.5 * 2000)

1/v = 147.5 / (12.5 * 2000)

1/v = 0.0059

v = 1 / 0.0059 = 169.5 cm

The height of the image formed by the mirror can be calculated using the magnification formula:

magnification (m) = v/u = height of image (h') / height of object (h)

Substituting the values, we have:

0.0059 = h' / 160

h' = 0.0059 * 160 = 0.944 cm

Therefore, the height of the image formed by the convex side mirror is approximately 0.944 cm.

Answer 2

(D) 0.99 cm

Step-by-step explanation:

Given that the radius of curvature of the mirror is 25 cm.

And another car is following which is behind the mirror of 20 m.

`u=20m=2000cm`

Focal length is half of the radius of curvature and it is negative for convex lens.

Now the mirror formula.

`1/v+1/u=1/f`

So,

`1/v+1/2000=-1/(25/2)\\1/v=-1/2000-1/12.5\\v=-12.422cm`

Now

Magnification is,

`m=-v/u`

So,

`m=12.422/2000=0.00621`

So, Height of the image

`mh=0.00621* 1.6 m\\mh=0.0099m\\mh=0.99cm`

Therefore, the image height is 0.99 cm.