Question

A source of light O is located at a distance of 8 cm from a plane mirror. The reflected ray O' is detected 2 cm from the mirror at a vertical displacement of 12 cm. The point of reflection is at a distance of


(A) 6.0 cm from X (B) 7.2 cm from X


(C) 2.4 cm from Y (D) 3.6 cm from Y​

Answer 1

According to laws of reflection (I think you presumably know it) that the angle of reflection is always is equal to angle of incidence .

∠i = ∠r which implies that :

⇒ 90° - ∠i = 90° - ∠r

This means that we can confidently say that ∠OPX = ∠O'PY [ See the figure once , don't be too lazy ] .

Let's see what we have got in ΔOPX and ΔO'PY . At the blink of an eye I can see that the two triangles are similar .

∠X = ∠Y [ 90° each ]

∠OPX = ∠O'PY [ as said above ]

Δ OPX ≈ Δ O'PY [ A.A criterion ]

Assume the distance is x cm from Y .

Then we have :

x / (12 - x) = 2/8

⇒ 8 x = 24 - 2 x

⇒ 8 x + 2 x = 24

⇒ 10 x = 24

⇒ x = 24/10

⇒ x = 2.4 cm

The distance is 2.4 cm from Y .

OPTION C is correct according to me , if incorrect then sorry .

P.S : Sorry for the attachment , did it in a hurry in Paint .

Answer 2

A source of light O is located at a distance of 8 cm from a plane mirror. The reflected ray O' is detected 2 cm from the mirror at a vertical displacement of 12 cm. The point of reflection Y is 9.085 cm from X, which is closest to option (A) 6.0 cm from X.

We can use the laws of reflection to solve this problem.

According to the laws of reflection,

the angle of incidence is equal to the angle of reflection,

the incident ray, the reflected ray, and the normal to the mirror all lie in the same plane.

Let X be the point on the mirror where the incident ray hits it,

Let Y be the point where the reflected ray hits it.

Let Z be the point where the normal from X to the mirror intersects the mirror.

Since O is 8 cm from the mirror,

The incident ray hits the mirror at a distance of 8 cm from the mirror.

This means that X is 8 cm from O.

Since the reflected ray is detected 2 cm from the mirror at a vertical displacement of 12 cm,

We can draw a right triangle with legs of length 2 cm and 12 cm.

The hypotenuse of this triangle is the distance between Y and Z.

By the use of Pythagorean theorem,

hypotenuse = sqrt(2^2 + 12^2) = sqrt(148) ≈ 12.17 cm

Since Y is 2 cm from the mirror and Z is on the mirror,

The distance between Y and Z is 10.17 cm.

Since the incident ray and the reflected ray are at equal distances from the mirror,

We can draw a line from O to Y that is perpendicular to the mirror.

This line will pass through the midpoint of X and Z.

The midpoint of X and Z is (8 + 10.17)/2 = 9.085 cm from X.

Therefore, the point of reflection Y is 9.085 cm from X, which is closest to option (A) 6.0 cm from X.

For similar questions on laws of reflection,

https://brainly.in/question/31867810

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