?When a concave mirror is placed facing the Sun, the Sun’s rays converge to a point 10 cm from the mirror. Now, if you place a 2 cm long candles flame 20 cm away on the principal axis of the mirror, where would you place a screen to obtain the image of the candle? What would see the size of the image? Draw a ray diagram to justify your answer.?

Question

Answer

Given:

Sunrays from Sun strike concave mirror and after reflection converges at a point Focus (F) on the principal axis.

So, focal length =f= -10cm.( by sign convention).

U= -20cm.

Mirror formula:

1/f=1/u+ 1/ v

1/v= 1/f-1/u

=1/-10 +1/20

=-2+1/20

V=-20cm.

Hence screen should be placed at a distance of 20cm from the mirror.

TO FIND NATURE OF IMAGE:

m=-v/u= hi/ho

hi=-(-20)/-20 X 2

hi=-2cm

SO, m = hi/ ho

m=-2/2

m=-1

Magnification is negative, THIS IMPLIES THAT image formed is real and inverted

m=1 IMPLIES that size of object equals to size of image.

Answer

Calculating the Image Position

Using the mirror formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

Since the mirror is concave, f is negative, and since the image is real, v is also negative.

Substituting the given values, we get: -1/f = 1/-10 + 1/-20

Solving for f, we get: f = -15 cm.

Using the magnification formula: m = -v/u, where m is the magnification.

Substituting the given values, we get: m = -(-10)/20 = 0.5.

Therefore, the image is half the size of the object.

Since the image is real and inverted, it will be formed on the same side of the mirror as the object.

Using the ray diagram, we can determine the exact position of the image.

Drawing the Ray Diagram

Draw the principal axis and mark the focal point F.

Draw the object AB, 20 cm away from the mirror on the principal axis.

Draw two parallel rays from point A: one parallel to the principal axis, and the other passing through the focal point F.

Draw a third ray from point A, which passes through the center of curvature C of the mirror.

The point where the three rays intersect is the image A'B' of the object AB.

Draw the image A'B' on the other side of the mirror, since it is real and inverted.

Measure the distance between the mirror and the image to find the image position.

Place the screen at the image position to obtain the image of the candle.

Conclusion

The image of the candle will be formed at a distance of 10 cm from the mirror.

The size of the image will be half the size of the object.

The ray diagram shows that the image will be real and inverted.

The screen should be placed at the image position to obtain the image of the candle.

Similar Class 10 Doubts

When object placed at between p and f infront of concave mirror ? Write the position ,size and nature of the image .draw its diagram?

A car headlight bulb contains two filaments A and B filament B is at the principle focus of the concave mirror Trace the diagram and draw rhe rays of light from each filament why is this arrangement used in car headlight?

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