Why is the Moon visible in the shadow of the Earth? Quantify

During the total phase of a lunar eclipse, the Moon is illuminated by the rays of the Sun refracted in the earth’s atmosphere. A ray of the Sun, tangent to the earth’s surface, is refracted towards the earth’s shadow at an angle equal to twice the refraction value, that is, at 35’x2 = 70 ‘(the standard value for middle latitudes). The angular diameter of the earth’s shadow is 84 ‘(average). Thus, the tangential rays of the Sun illuminate the Moon during almost the entire shadow eclipse. The rays passing through the upper layers of the earth’s atmosphere are refracted less, but also bent into the earth’s shadow.

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