She had told him that she had spells of being terribly lonesome.
Jack had an inspiration.

He climbed hurriedly down off the rock, got his own looking glass and climbed back again.

He turned the glass so that the sun shown on it aslant and threw a glare toward her.

Then he lifted the telescope quickly to see if she noticed the sparkle.

After a moment he decided that she had seen it but did not quite know what had caused it.