Question

A real image of half the size of the objectis produced by a spherical mirror .on moving the object away from the mirror by 0.30 m ,the size of the image become 1/3 that of object .calcute the radius of curvature of the spherical mirror

Answer 1

The mirror produces three times enlarged image.

So, magnification(m) = 3

WE KNOW, magnification of spherical mirrors = m = -v/u

Where v is the distance between image and mirror and u is the distance between object and mirror.

Here, u = -10 cm

=> 3 = -V/-10

=>v = 30

So , the distance between image and mirror = 30 cm

1/v + 1/u = 1/f(mirror formula)

1/30 + 1/-10 = 1/f

1/30 - 1/10 = 1/f

-2/30 = 1/f

-1/15 = 1/f

f = -15 cm

We know radius of curvature = 2f

So, radius of curvature = R = 2*-15 = -30 cm which is the required answer.

SHORTCUT -

Remember the formula, m = f/(f-u)

So, 3 = f/(f-(-10))

3 = f/(f+10)

Cross multiply,

3f + 30 = f

2f = -30

R = -30 cm (R= 2f).

Answer 2

The Radius Of Curvature Or The Spherical Mirror Is -3.33 meter.

GIVEN

Size of the image = half the size of the object.

Distance by which the object is moved = 0.30 meter

Size of the image = one-third the size of the object.

TO FIND

The radius of curvature of the mirror.

SOLUTION

We can simply solve the above problem as follows-

We know that magnification can be defined as the ratio of the distance of the image to the distance of the object.

So,

m = -v/u

It is given, that the image size is half of that of the object size.

Also,

m = hi/ho = 1/2

where,

hi = height of the image

ho= height of the object

So,

-v/u = 1/2

u = -2v (equation 1)

When the object moved by 0.30 meters the size of the image was 1/3 of the object's size.

m = -v/u+0.3 = 1/3

u + 0.3 = -3v. (Equation 2)

From equation 1 and equation 2

-3v = -2v + 0.3

v = -0.3 meter.

Putting the value of 'v' in equation 1

u = -2(-0.3)

u = 0.6 meter.

Now we know that,

The radius of curvature, r = 2f

Where, f = focal length.

Now applying the mirror formula -

1/f = 1/u + 1/v

1/f = 1/0.6 -/0.3

1/f = -1/0.6

f = -1.66 meter

so,

r = 2 × -1.66

= -3.33 meter

Hence, the radius of curvature or the spherical mirror is -3.33 meter.

#spj2

For more such questions -

https://brainly.in/question/8109481?utm_source=android&utm_medium=share&utm_campaign=question

https://brainly.in/question/14599250?utm_source=android&utm_medium=share&utm_campaign=question