Mirror, Mirror on the Wall

D. Leela and classmates

It was a sunny Saturday afternoon. Nivedita came up the stairs and rushed into the room where all the noise was going on. Leela and Sanjana were dancing and tapping to the music of Kaali Megha from the film Lagaan. Maya was holding a small mirror in her right hand and shouting, "Left, right, left, right" at the top of her voice. As she shouted, she thrust out her left hand, first to the left, then to the right, with a comically serious expression on her face.
"Hi Nivedita!" said Leela. "Finished your homework?" "Yes, all done," replied Nivedita. "How about you?" 
Leela said, "Oh, we both have finished. Only Maya hasn't finished as yet." Nivedita turned to Maya, who was still punching the air and shouting. "Maya, why don't you stop fooling around and finish your homework? Then we can all go and play downstairs." 
Maya stopped punching with her left hand and waved the mirror instead. "I am doing my homework," she proclaimed proudly. I am learning "Left" and "Right". Look!", she said, pointing at the mirror: I am looking into the mirror and then I know left from right!" 
Nivedita said, "But, Maya, a mirror will not tell you left from right. In fact, if you lift your right hand, it will look like your left hand in the mirror." She turned to Leela. "Leela, why don't you teach her properly? She's getting it wrong!" 
Leela said, "No, no, she's got it right ... I mean she's doing it correctly." Delighted with herself at her own pun, she continued, "See, Maya is standing with her back to the big mirror on the wall. When she looks into the small mirror, she's actually looking at the reflection of herself in the big mirror." 
Nivedita paused to take in all the mirrors. Sure enough, Maya was looking at the small mirror, but holding it so that she was not seeing her own hand directly, but actually seeing the reflection of herself in the big mirror. Sanjana stopped swaying and looked up to ask, "But how does that make a difference? A mirror always interchanges left and right. I see that every day, I don't have to learn it in school." 
Leela said, "I don't know why it happens, but my mother showed it to me when I was very small. If you look at yourself through two sets of mirrors, this way, right remains right and left remains left." 
Nivedita said, "Sure, you're right! That's smart. Actually, what happens is that the first reflection interchanges left and right. But the second reflection interchanges it once more, so left becomes left again." 
By now Maya had lost interest in the long explanation and was dancing to the music in front of the big mirror. Sanjana was amused. She said, "Maya, ask your mother for a big mirror so you can see yourself dancing in it. You'll really enjoy it. This mirror is too small to see yourself fully." 
Maya said, "No, I can see myself fully. See how nicely the nailpolish is shining on my toes!" Sanjana said, "No, Maya, when you see your toes, you have to bend over and then you can't see your face at the same time. This mirror is too small." She stepped closer to the mirror and then stepped back again. "No," she repeated. It doesn't help to come closer or go farther away. The mirror is too small." 
Maya said, "No. No. No. I can see all of myself in the mirror." "That's because she's got short legs," joked Leela. "She's just a child," Nivedita said. "Don't tease her. If she's enjoying herself, what's the problem even if she can't see herself fully?" 
"No-one believes me," sobbed Maya. As she saw the tears pouring down her reflection in the mirror, she cried even louder.
"Girls, girls, what's happening?" asked Amma from the doorway. "You know that Poorna Aunty next door likes her afternoon nap." Everyone rushed to explain. "Okay, okay," said Amma. "What a commotion over nothing!" 
All the girls looked expectantly at her. "Let's do this systematically. Leela, go and get the tape-measure. Let's measure some heights here." 
As Leela rushed off to get the tape, Sanjana asked, "But, Aunty, she can't really see herself fully, can she? I mean, look, the mirror is hardly half her height! How can she ...?" 
"Wait," said Amma, impressively. Leela came rushing back with the tape. "Me first," yelled Maya. "OK," said Amma. "Measure the mirror's height." Maya took the tape and held one end against the top of the mirror. Sanjana kneeled down and read off the height from the other end. "50 cm," she announced. Then she turned and looked at Maya. "You can't be 50 cm tall," she giggled. "Why, even babies are bigger, I would think!" 
"Shush", said Amma. "Now let's measure Maya." Sanjana held the tape to Maya's head and Leela held it to the ground. "95 cm", said Leela, reading off the number on the tape. Amma exclaimed, "Maya, you've grown! I never realised it." She turned to the other children and smiled. "You know, Maya is right. She can indeed see all of herself in the mirror!" 
There was a babble of words from all. "It can't be!" "I told you so!" Then Nivedita's voice asked, "Aunty, how can it be?" 
"Good question," said Amma. "You have learnt the laws of reflection in school?" As Nivedita nodded, she went on. "Then you must know that when light falls on a mirror and is reflected from it, the angle of incidence equals the angle of reflection. So, for instance, the light rays from your feet come up at an angle, hit the mirror, and then fall into your eye after getting reflected at the same angle." (See figure).
"Because of this," continued Amma, "you only need half the size of the mirror as yourself to see yourself fully. Now, Maya is 95 cm tall and the mirror is 50 cm high. Are you convinced that she can indeed see herself fully?" 
Maya looked around proudly. Leela said disgustedly, "Any one would think she actually understood all that about laws of reflection!" Amma smiled. "Well, you older children were only convinced by my explanation. Maya was convinced for the best reason of all! Do you know what it is?" 
"Because you said so?" asked Sanjana, curiously. "No," laughed Amma. "Because she is the only one small enough to actually stand there and see for her self that this is so!" 
"I knew it, her legs are too short," said Leela, sulkily. Before Maya could protest, Amma said hurriedly. "Do you know what Abraham Lincoln said when he was asked how long a person's legs should be?" "No, what did he say?" asked all the children curiously.
"He said that a person's legs should be long enough to reach from his body to the ground!" said Amma. Every body in the room collapsed in a heap of laughter.