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Dusk is when it is dark, or when the reddishness in the sky ends. The dictionary defines dusk as the darker stages of twilight

To determine Isha and Fajr calculations, one needs to calculate the time when the sun is at a certain distance below the horizon. The twilight angle is used for this purpose and it is defined as the angle in degrees of the sun below the horizon, when total darkness begins or ends.
Some organisations use a fixed time after Maghrib to determine the start of Isha time

The following standards exist for determining Fajr and Isha times:

Organisation Fajr – twilight angle Isha – twilight angle Region
Muslim world league 18 17 Europe, Far East, parts of the USA
Egyptian General Authority of Survey 19.5 17.5 Africa, Syria, Iraq, Lebanon, Malaysia, parts of the USA
Islamic Society of North America (ISNA) 15 15 Parts of the USA, Canada, parts of the UK
University of Islamic sciences, Karachi 18 18 Pakistan, Bangladesh, India, Afghanistan, parts of Europe
Umm Al Qura 19 90 minutes after Maghrib (120 minutes during Ramadan) The Arabian Peninsula

Twilight is the name given to the light that is observed after sunset and before sunrise. At this point the sun is below the horizon.

The times of the prayer are determined by the position of the sun, i.e. by defining the above in astronomically measurable terms. However for countries above 48 degrees (including Britain), Fajr and Isha timings require some estimation as the twilight may persist between sunset and sunrise for certain months of the year. In these months the sun does not go below the horizon by a sufficient amount and so there is no true night. Under these circumstances Salahtimes uses the 1/7 rule method by default (for UK) to calculate the Fajr and Isha times respectively, although you can change this to an alternative method.

Muslims pray 5 times a day. The times of each prayer vary from place to place and from day to day. It is vital that Muslims perform these prayers at the correct time
The 5 prayers are described below:

Fajr:
Starts at dawn or morning twilight
Ends just before sunrise

Zohar:
Starts at approximately 5 minutes after Zawaal
Ends at start of Asar time

Asar:
The start of Asar is dependant upon the length of the shadow that is cast by an object. Different schools use different criteria.
Ends just before sunset

Maghrib:
Starts at sunset
Ends at the start of Isha (i.e. when there is reddishness in the sky)

Isha:
Starts after dusk
Ends when the evening twilight disappears (i.e. when it first starts to get light)