It is with the lamp before the baby's face that Mrs. Keller proves without a doubt what has happened to her baby.

As Mrs. Keller screams for him, Keller runs up the stairs to her. 

KELLER: Katie? What’s wrong?

KATE: Look […] She can’t see. Look at her eyes.

(She takes the lamp from him, moves it before the child’s face.)

She can’t see!

Throughout the story, Helen lives in a world of darkness, not only literally because she cannot see, but also in that she is cut off from the world with no way to communicate.

At the end of Act Two, Annie Sullivan has convinced the Kellers to allow her to take Helen to the hunting cottage in an attempt to break through Helen's darkness—not her blindness, but the prison her blindness—and deafness—have created around the child.

At two o'clock in the morning (when it is dark), Annie decides to try to teach Helen, but Helen won't allow her teacher to touch her in order to sign letters into her hand. The darkness of the hour symbolizes not simply Helen's blindness, but also her lack of knowledge, Annie's frustration and perhaps even an ebbing hope that she will ever reach her student. Certainly the situation seems hopeless in that Annie cannot make any progress at the homestead with others interfering and coddling Helen regardless of her terrible behavior.

When Annie lights a match for the lamp, this symbolizes the coming of hope. Since Helen cannot abide Annie's touch, her teacher calls to Percy and places letters in his hand. Helen is curious but still resists Annie's touch. So Annie continues to spell to Percy until enraged, Helen bodily pushes Percy away:

(Helen now yanks their hands apart. She butts Percy away, and thrusts her palm insistently. Annie's eyes are bright with glee.)

Ho, you're jealous, are you!

(Helen's hand waits, intractably waits.)

All right.

(Annie begins to spell into Helen's hand, and Helen allows it.)

Good! So I'm finally back to where I can tough you, him? Touch and go! No love lost, but here we go.

At the play's end, when Helen and Annie are at the pump and Helen finally connects the word with the thing, light is used to symbolize illumination again.  State direction notes:

And now the miracle happens. Helen drops the pitcher on the slab under the spout...She stands transfixed. Annie freezes on the pump handle. There is a change in the sundown light, and with it a change in Helen's face, some light coming into it we have never seen there...

It is at this point that Helen remembers and forces out the baby word she once knew for "water." In this the audience understands that Helen now knows that the words Annie has been teaching her represent things in the world around her.

Interestingly, the stage lighting in the story supports the symbolism of light and darkness. At the moment of Helen's awareness, there is a change in the stage's "sundown light."

Light is referred to yet again in Helen's face, symbolizing the light of knowledge.

In The Miracle Worker by William Gibson, Gibson uses symbols to connect the abstract nature of Helen's struggles to the concrete reality of her world. Darkness and light are common symbols in many works because they have deep significance, bridging the gap between what is apparent on the surface where a person can actually see and what a situation really reveals. Similarly, it is Annie Sullivan's ability to "see" what is needed and figuratively "unlock" Helen's mind, and so provide a means of communication, upon which this play revolves.  Based on Helen Keller's "miracle" in the form of Annie Sullivan, the play shows how even those who have their sight can lack perceptive skills and good judgment, resulting in poor decision-making (the family has never tried to discipline Helen) and often it requires an external influence or even, as Captain Keller would presume, in this case, interference to make a situation clear. 

There are many instances in the play where the audience is encouraged to reflect and envision life in Helen's darkness. One instance when Gibson uses darkness and light symbolically comes right at the beginning of Act I. The play opens during the night and the night symbolizes helplessness, foreshadowing what will follow. There is only a dim lamp light by which to see. This is representative of the situation before Annie arrives. The doctor suggests that the family rests especially as it has been by Helen's bedside during her illness. The fact that people sleep during the night (the darkness) and the family has been deprived of sleep (therefore remaining in the dark without the benefit of restful sleep) is significant. In the real and the symbolic darkness, the doctor and the family cannot begin to understand the significance of recent events or what is about to unfold. There is potential (the light is lit after all, even though it is dim) but it will remain unrealized without Annie's intervention.

Kate tells her husband to "Look" when she realizes that something is wrong with Helen, but notably, Helen does not respond to the light of the lamp (note the symbolism of this) as Kate holds it in front of Helen's face. Light is revelation. It is ironic that Annie, a partially-sighted person herself, is the one who will provide the link between the real darkness which, for Helen, will never change and the whole family's future which will most definitely change as Annie guides Helen and her family towards the light in the form of success.