Two dielectric media with dielectric constants ε1 and ε2 are separated by a plane boundary...

Two dielectric media with dielectric constants ε1 and ε2 are separated by a plane boundary at x = 0, as shown in Fig. A point charge Q exists in medium 1 at distance d from the boundary.

Figure: Image charges in dielectric media

a) Verify that the field in medium 1 can be obtained from Q and an image charge -Q1, both acting in medium 1.

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b) Verity that the field in medium 2 can be obtained from Q and an image charge +Q2 coinciding with Q, both acting in medium 2.

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c) Determine Q1 and Q2 (Hint: Consider neighboring points P1and P2 in media 1 and 2, respectively, and require the continuity of the tangential component of the E-field and of the normal component of the D-field.)