Question

a 2 cm high object is placed perpendicular to principal axis of the concave mirror the distance of the object from the mirror is 30 cm and its image is formed at 60cmfrom the mirror on the same side of the mirror as the object find focal length and draw ray diagram
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Answer 1

Answer:

Given:

• We have been given that the object distance(u) = -30cm, image distance(v) = -60cm.
• We have also been given that the height of object is 2cm. And it is placed perpendicular to the principle axis.

To Find:

• We need to find the focal length of the mirror.

Solution:

We have been given the object distance(u) = -30cm and image distance(v) = -60cm.

So we can find the focal length of the mirror by the mirror formula:

1/v + 1/u = 1/f

Substituting the values, we have

(1/-60) + (1/-30) = 1/f

=> [-30 + (-60)/1800] = 1/f

=> (-30 - 60)/1800 = 1/f

=> -90/1800 = 1/f

=> 1/-20 = 1/f

=> f = -20cm

Therefore, the focal length of the mirror is -20cm.

Answer 2

Given :

▪ Distance of object = u = -30cm

▪ Distance of image = v = -60cm

▪ Height of object = h = 2cm

▪ Type of mirror = concave

To Find :

▪ Focal length of concave mirror.

Solution :

✒ We can easily solve this type of questions with the help of mirror formula.

✒ Mirror formula shows relation between u, v and f.

✴ Mirror formula :

☞ 1/u + 1/v = 1/f

____________________________

• u = -30cm
• v = -60cm
• f = ?

Substituting given values, we get

→ -1/30 + (-1/60) = 1/f

→ -2/60 - 1/60 = 1/f

→ -3/60 = 1/f

→ f = -60/3

→ f = -20cm

▶ See the attachment for ray diagram.

____________________________

✴ Additional information :

✏ Magnification = h'/h = -v/u

• h' = height of image
• h = height of object

▪ h'/2 = -(-60/-30)

▪ h'/2 = -2

▪ h' = -4cm

⏭ Nature of image :

• Real
• Inverted

⏭ Size of image :

• Enlarged