The concave mirror shown below has an object placed 20cm in front of it. An image is formed in 35 cm in front of the mirror. What is the nature of the image? Calculate the magnification of the image and the focal length of the mirror

The concave mirror that has an object placed 20cm in front of it. and an image is formed at 35 cm in front of the mirror.

The nature of the image formed is

(i) It is Formed beyond C

(ii) It is enlarged

(iii) It is magnified

The magnification is 1.75

The Focal length of the mirror is 12.73 cm

From the question, we need to calculate the focal length of the mirror using mirror formula.

1/f = (1/v)+(1/u) Eqaution 1

Where f = focal length, v = object distance, u = image distance.

From the question,

Given: v = 20 cm, u = 35 cm

Substitute these values into equation 1

1/f = (1/20)+(1/35)

1/f = (20+35)/(20×35)

f = (20×35)/(20+35)

f = 700/55

f = 12.73 cm.

Hence the mirror focal length is 12.73 cm

Since the mirror is placed between F and C in a concave mirror

The nature of the image formed is

(i) It is Formed beyond C

(ii) It is enlarged

(iii) It is magnified

Finally,

magnification = image distance/object distance = D/D'

mag = 35/20

mag = 1.75.

Hence the magnification of the image is 1.75

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image is real, Inverted and magnified

Focal length of the mirror is 12.7 cm

Explanation:

As we know that object is placed at distance 20 cm in front of mirror and its image formed at 35 cm in front of mirror

So here since object and image both are on same side of mirror so this must be REAL image

now we know that magnification is given as

so image is real, Inverted and magnified

now for focal length of the mirror we can use the equation

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double the distance = divide strength by 4