Question

What is the smallest size of a looking glass, a person with a face 24 cm by 16 cm should
purchase, which will enable him to see his whole face at a time. The distance between his
eyes is 8 cm
A) 24 cm by 16 cm B) 12 cm by 8 cm c) 12 cm by 4 cm D) 6 cm by 2 cm​

Answer 1

Answer:

half the dimensions are enough so 12cm by 8cm

Answer 2

Answer:

The smallest size of a looking glass mirror is 12cm by 4cm

Explanation:

Given:

• A person with a face 24 cm by 16 cm looking through the glass .
• The distance between his eyes is 8 cm

To find: The smallest size of the mirror

Solution:

Smallest length of the mirror = Half the length of face

   = $\frac{1}{2} (24)$

height = 12 cm

Smallest breadth of the mirror is calculated using the condition the rays from external part of face should reach one the eye after reflection from the mirror.

The common overlapping portion of the mirror is the required size.

The ray  diagram has shown below

From the given figure,

$MM' = \frac{1}{2} PQ - \frac{1}{2} E_{1} E_{2}$

    $= \frac{1}{2} (16 - 8)$

    $= \frac{1}{2} (8)$

    = 4 cm

Shortest size of the mirror is 12cm by 4cm

Final answer:

The smallest size of a looking glass mirror is 12cm by 4cm

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